United States Office of Research and EPA/600/R-02/001

Environmental Protection Development May 2002

Agency Washington, D.C. 20460 www.epa.gov/ncea

Research and Development

The QTRACER2 Program for

Tracer-Breakthrough Curve

Analysis for Tracer Tests

in Karstic Aquifers and

Other Hydrologic Systems

(Supersedes EPA/600/R-98/156a and 156b, 2/’99) 
EPA/600/R-02/001

May 2002

The QTRACER2 Program for TracerBreakthrough Curve Analysis

for Tracer Tests in Karstic Aquifers

and Other Hydrologic Systems

(Supersedes EPA/600/R-98/156a and 156b, 2/’99)

National Center for Environmental Assessment–Washington Office

Office of Research and Development

U.S. Environmental Protection Agency

Washington, DC 20460
DISCLAIMER

This document has been reviewed in accordance with U.S. Environmental Protection Agency

policy and approved for publication. Mention of trade names or commercial products does

not constitute endorsement or recommendation for use.

ii
Contents

LIST OF TABLES

LIST OF FIGURES

PREFACE

AUTHOR and REVIEWERS

ABSTRACT

1. INTRODUCTION

viii

ix

xii

xiii

xiv

1

1.1. LIMITATIONS OF THIS REPORT .... ........... ........ 1

1.1.1. Li mi tati ons Related to Type of Tracer ......... ........ 1

1.1.2. Types of Appli cable Hydrologi cal Systems ...... . ........ 1

1.1.3. Quanti tati ve Versus Quali tati ve Tracer Tests ...... ........ 2

1.1.4. Li mi tati ons Based on Test Desi gn . ........... ........ 2

1.2. PURPOSE ....... ........... ........... ........ 2

1.2.1. Quantitative Tracer Tests to Support Ground-Water Monitoring Efforts 3

1.2.2. Quanti tati ve Tracer Tests for Ri sk Assessments ... . ........ 3

1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation 5

1.3. QUALITATIVE VERSUS QUANTITATIVE TRACING . . . ........ 5

2. TRACER TEST DESIGN FACTORS 8

2.1. TRACER CHARACTERISTICS ..... ........... ........ 11

2.2. TRACER INJECTION ........... ........... ........ 13

2.2.1. Methods of Injecti on ........ ........... ........ 13

2.3. TRACER SAMPLING ........... ........... ........ 18

2.4. SAMPLING EQUIPMENT ........ ........... ........ 19

2.5. SAMPLING LOCATIONS AND FREQUENCIES ...... . ........ 19

2.6. TRACER MIXING IN THE FLOW SYSTEM ........ . ........ 20

2.7. CORRECTION FOR TIME TO REACH FLOW SYSTEM . . ........ 20

2.8. CORRECTION FOR BACKGROUND . . ........... ........ 21

2.9. DISCHARGE MEASUREMENTS ..... ........... ........ 22

2.10. KARST CONDUIT NETWORKS ..... ........... ........ 23

2.10.1. Network Types I, II, and III .... ........... ........ 23

2.10.2. Network Types IV and V ...... ........... ........ 23

2.10.3. Network Types VI and VII ..... ........... ........ 25

2.11. DETERMINATION OF TOPOLOGICAL KARST CONDUIT NETWORK

TYPE ......... ........... ........... ........ 25

iii
3. QUANTITATIVE TRACING METHODOLOGY 26

3.1. ESTIMATION OF HYDRAULIC PARAMETERS ..... . ........ 27

3.1.1. Total Tracer Recovery ....... ........... ........ 29

3.2. QUALITY OF TRACER MASS RECOVERY ........ . ........ 29

3.2.1. Mean Resi dence Ti me ....... ........... ........ 30

3.3. Resi dence Ti me Skewness and Kurtosi s . . ........... ........ 32

3.3.1. Mean Tracer Veloci ty ........ ........... ........ 32

3.3.2. Longi tudi nal Di spersi on ...... ........... ........ 34

3.3.3. Tracer Di luti on ........... ........... ........ 38

3.4. FLOW-CHANNEL GEOMETRIES .... ........... ........ 39

3.4.1. Aqui fer Volume ........... ........... ........ 40

3.4.2. Cross-Secti onal Area ........ ........... ........ 41

3.4.3. Flow-Channel Di ameter ...... ........... ........ 41

3.4.4. Flow-Channel Hydrauli c Depth . . ........... ........ 41

3.4.5. Flow-Channel Surface Area .... ........... ........ 41

3.4.6. Tracer Sorpti on Esti mati on .... ........... ........ 42

3.5. EMPIRICAL FLUID DYNAMICS MODELS ......... . ........ 42

3.5.1. P ́eclet Number ........... ........... ........ 43

3.5.2. Dynami c Flow Equati ons ...... ........... ........ 43

3.6. BOUNDARY-LAYER EFFECTS ..... ........... ........ 45

3.6.1. Fri cti on Factor Esti mati on ..... ........... ........ 45

3.6.2. Viscous-Flow Sublayer ....... ........... ........ 46

3.6.3. Hydrauli c Head Loss ........ ........... ........ 46

3.6.4. Shear Veloci ty . ........... ........... ........ 47

4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY 48

4.1. SIMPLIFIED EXAMPLE CALCULATION ......... . ........ 50

4.1.1. Mass Recovery Example ...... ........... ........ 51

4.1.2. Mean Resi dence Ti me Example . . ........... ........ 51

4.1.3. Mean Tracer Veloci ty Example . . ........... ........ 54

4.1.4. Longi tudi nal Di spersi on Example . ........... ........ 54

4.1.5. System Volume ........... ........... ........ 56

5. QTRACER2 COMPUTER PROGRAM DESCRIPTION 58

5.1. DATA INTERPOLATION ......... ........... ........ 58

5.2. DATA EXTRAPOLATION ........ ........... ........ 58

5.2.1. Exponenti al Decay ......... ........... ........ 58

5.2.2. Piecewise Cubic Hermite ...... ........... ........ 59

5.2.3. Strai ght-Li ne Projecti on ...... ........... ........ 59

5.2.4. Extrapolati ng Di scharge ...... ........... ........ 59

5.3. CHATWIN’S ESTIMATION OF LONGITUDINAL DISPERSION ..... 59

5.4. DATA NORMALIZATION ......... ........... ........ 60

5.5. RANGE OF POSSIBILITIES OF QTRACER2 ....... . ........ 60

5.6. COMPUTER GRAPHICS ......... ........... ........ 61

iv
5.6.1. Features of the Interacti ve Graphi cs Loop ...... . ........ 61

5.7. QTRACER2 SOURCE ........... ........... ........ 64

6. USING QTRACER2 65

6.1. QTRACER2 PROGRAM AND EXAMPLE DATA FILES . . ........ 65

6.1.1. Loadi ng QTRACER2 and Example Data Fi les .... . ........ 65

6.2. QTRACER2 EXECUTION ........ ........... ........ 66

6.3. QTRACER2 FUNCTIONING....... ........... ........ 67

6.4. SAMPLE FILES ON DISK ........ ........... ........ 67

6.5. DESCRIPTION OF *.D FILES ...... ........... ........ 69

6.6. DESCRIPTION OF *.DAT FILES .... ........... ........ 72

6.6.1. Sampli ng Frequency ........ ........... ........ 72

6.6.2. Tracer Mass Recovery ....... ........... ........ 72

6.6.3. Flag for Background ........ ........... ........ 72

6.6.4. Measured Di scharge ........ ........... ........ 76

6.6.5. Di scharge Uni ts ........... ........... ........ 76

6.6.6. System Volume ........... ........... ........ 77

6.6.7. Radi al Di stance ........... ........... ........ 78

6.6.8. Correcti on for Si nuosi ty ...... ........... ........ 78

6.6.9. Flow Medi um . ........... ........... ........ 78

6.6.10. Porous-Medi a and Fracture Uni ts . ........... ........ 79

6.6.11. Output Fi le Name ......... ........... ........ 79

6.6.12. Sample Data Interpolati on ..... ........... ........ 79

6.6.13. Interpolated Data Fi le Name .... ........... ........ 80

6.6.14. Sample Data Extrapolati on .... ........... ........ 80

6.6.15. Vi suali ze Ori gi nal Data ....... ........... ........ 81

6.6.16. Vi suali ze Interpolated Data .... ........... ........ 82

6.6.17. Vi suali ze Chatwi n Parameters ... ........... ........ 83

6.6.18. CXTFIT2.0 Data Fi le Creati on . . ........... ........ 83

6.6.19. Normali zed Tracer Concentrati on . ........... ........ 84

6.6.20. Normali zed Tracer Load ...... ........... ........ 85

6.6.21. Standardi zed Data Fi le ....... ........... ........ 86

6.6.22. Screen Di splay ........... ........... ........ 87

6.6.23. Method for Handli ng Large Ti me-Concentrati on Data Fi les ...... 87

6.6.24. Actual Ti me-Concentrati on Data . ........... ........ 88

7. EXAMPLE ANALYSES FROM QTRACER2 90

7.1. QTRACER.D EXAMPLE OUTPUT ... ........... ........ 90

7.1.1. QTRACER.DAT Tracer-Breakthrough Curve .... . ........ 91

7.1.2. QTRACER.DAT Chatwi n Plot . . ........... ........ 91

7.1.3. QTRACER.DAT Output Fi le ... ........... ........ 91

7.1.4. QTRACER.DAT Normali zed Tracer Concentrati on . . ........ 91

7.1.5. QTRACER.DAT Normali zed Tracer Load ...... . ........ 91

7.1.6. QTRACER.DAT Standardi zed Ti me-Concentrati on Data ....... 91

v
7.2. RCA.D EXAMPLE OUTPUT ....... ........... ........ 102

7.2.1. RCA.DAT Tracer-Breakthrough Curve ........ . ........ 102

7.2.2. RCA.DAT Chatwi n Plot ...... ........... ........ 102

7.2.3. RCA.DAT Output Fi le ....... ........... ........ 102

7.2.4. RCA.DAT Normali zed Tracer Concentrati on ..... . ........ 102

7.2.5. RCA.DAT Normali zed Tracer Load ........... ........ 102

7.2.6. RCA.DAT Standardi zed Ti me-Concentrati on Data . . ........ 112

7.3. ANALYSIS ASSESSMENT OF THE QTRACER AND RCA EXAMPLE

DATA FILES ..... ........... ........... ........ 112

7.3.1. Molecular Di ffusi on Layer Thi ckness .......... ........ 112

8. QTRACER ANALYSIS OF OTHER HYDROLOGICAL SETTINGS 115

8.1. SURFACE-WATER AND POROUS-MEDIA EXAMPLES . . ........ 115

8.1.1. Surface-Water Example ...... ........... ........ 115

8.1.2. Porous-Medi a Example ....... ........... ........ 124

9. DATA INTERPOLATION AND EXTRAPOLATION EFFECTS 132

9.1. COMPARISON OF QTRACER.DAT OUTPUT FILES ... . ........ 132

9.1.1. Interpolated QTRACER.DAT BTC ........... ........ 132

9.1.2. Interpolated QTRACER.DAT Chatwi n Plot ..... . ........ 132

9.1.3. Extrapolated QTRACER.DAT BTC ......... . ........ 138

9.1.4. Extrapolated QTRACER.DAT Chatwi n Plot ..... . ........ 138

9.2. INTERPOLATED-EXTRAPOLATED QTRACER.DAT DATA ....... 138

9.3. COMPARISON OF RCA.DAT OUTPUT FILES ...... . ........ 143

9.3.1. Interpolated RCA.DAT BTC ... ........... ........ 143

9.3.2. Interpolated RCA.DAT Chatwi n Plot .......... ........ 143

9.3.3. Extrapolated RCA.DAT BTC ... ........... ........ 147

9.3.4. Extrapolated RCA.DAT Chatwi n Plot ........ . ........ 149

9.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA . . . ........ 149

10. ASSOCIATED COMPUTER PROGRAMS 154

10.1. NDATA COMPUTER PROGRAM .... ........... ........ 154

10.1.1. NDATA Source ........... ........... ........ 155

10.2. AUTOTIME COMPUTER PROGRAM . ........... ........ 155

10.2.1. AUTOTIME Source ........ ........... ........ 155

10.3. DATFILE COMPUTER PROGRAM ... ........... ........ 158

10.3.1. DATFILE Source .......... ........... ........ 158

10.4. COMBINE COMPUTER PROGRAM . . ........... ........ 158

10.4.1. COMBINE Screen Plotti ng .... ........... ........ 163

10.4.2. COMBINE Processi ng ....... ........... ........ 170

10.4.3. COMBINE Source ......... ........... ........ 170

11. CONCLUSIONS 171

vi
NOTATION 172

REFERENCES 175

vii
List of Tables

1 Some commonly used fluorescent dye types ........... ........ 8

2 Data on some common fluorescent tracer dyes. ......... ........ 10

3 Percent pure dye content for selected fluorescent dyes. ..... ........ 18

4 Table representi ng tracer recovery data for processi ng. ..... ........ 48

5 Table representi ng tracer recovery data for processi ng. ..... ........ 49

6 Table representi ng Chatwi n values. .... ........... ........ 50

7 Di scharge values and tracer recovery values at speci fic ti mes. . ........ 53

8 Chatwi n parameter values for the RCA data set. ....... . ........ 55

9 Table of values used to determi ne the ti me of travel vari ance. . ........ 57

10 Pull-down menu i tems avai lable i n QTRACER2. ........ ........ 62

11 Example data files on di sk ......... ........... ........ 68

12 Estimated parameters from BTCs for QTRACER.DAT sampli ng stati on ..... 135

13 Estimated parameters from BTCs for RCA.DAT sampli ng stati on ....... 146

viii
List of Figures

1 Contami nant leakage i nto a si nkhole ... ........... ........ 4

2 A Turner DesignsR Model 10AU field filter fluorometer ... . ........ 6

3 Chemical structures for selected fluorescent dyes used for water tracing . . . 9

4 Electromagneti c spectrum for tracer dyes . ........... ........ 11

5 Reinforced sinkhole receiving plant waste water at RCA del Caribe ..... 14

6 Di ssoluti onally enlarged fissure i n li mestone ......... . ........ 15

7 Mi xi ng fluorescei n powder dye wi th water i n a 5 L carboy . . . ........ 16

8 Injecti ng mi xture of water and fluorescei n dye i nto an i njecti on well ..... 17

9 Typi cal response curves observed laterally and downstream . . ........ 21

10 Seven si mple karst network types that descri be tracer mi grati on ....... 24

11 Defini ti on sketch of BTCs along a selected tracer streamli ne . ........ 27

12 Lateral mi xi ng and longi tudi nal di spersi on patterns ..... . ........ 35

13 Tracer-breakthrough curve for the RCA de Cari be Superfund si te ...... 52

14 QTRACER.D header file for QTRACER2 processi ng ...... . ........ 70

15 QTRACER.DAT sampli ng stati on data file for QTRACER2 processi ng ..... 73

16 Tracer-breakthrough curve for the QTRACER.DAT data file ... ........ 92

17 Plot and straight-line fit of the Chatwin parameter for QTRACER.DAT ..... 93

18 Output file for the QTRACER.DAT sampli ng stati on data file . . ........ 94

19 Normalized tracer concentration data for the QTRACER.DAT data file ..... 99

20 Normalized tracer load data for the QTRACER.DAT data file . . ........ 100

21 Standardized time-concentration data for the QTRACER.DAT data file ..... 101

22 Tracer-breakthrough curve for the RCA.DAT sampli ng stati on data file .... 103

23 Plot and straight-line fit of the Chatwin parameter for RCA.DAT ....... 104

24 Output file for the RCA.DAT sampli ng stati on data file ..... ........ 105

25 Normalized tracer concentration data for the RCA.DAT data file ........ 110

26 Normalized tracer load data for the RCA.DAT data file ..... ........ 111

27 Standardized time-concentration data for the RCA.DAT data file ........ 113

28 Tracer-breakthrough curve for the UVAS281.DAT data file ... ........ 117

29 Plot and straight-line fit of the Chatwin parameter for UVAS281.DAT ..... 118

30 Output file for the UVAS281.DAT sampli ng stati on data file . . ........ 119

31 Tracer-breakthrough curve for the MOBILE.DAT data file .... ........ 125

32 Plot and straight-line fit of the Chatwin parameter for MOBILE.DAT ..... 126

33 Output file for the MOBILE.DAT sampli ng stati on data file.. . ........ 127

34 Interpolated curve for the QTRACER.DAT sampli ng stati on data file ...... 133

35 Interpolated data for the Chatwin parameter for QTRACER.DAT ........ 134

36 Extrapolated curve for the QTRACER.DAT sampli ng stati on data file ...... 139

37 Extrapolated data set for the Chatwin parameter for QTRACER.DAT ...... 140

38 Interpolated and extrapolated data set for the QTRACER.DAT data file .... 141

39 Interpolated and extrapolated data for the Chatwin parameter for the

QTRACER.DAT data file ........... ........... ........ 142

40 Interpolated curve for the RCA.DAT sampli ng stati on data file . ........ 144

41 Interpolated data for the Chatwin parameter for RCA.DAT ... ........ 145

ix
42 Extrapolated curve for the RCA.DAT sampli ng stati on data file ........ 148

43 Extrapolated data set for the Chatwin parameter for RCA.DAT ........ 150

44 Interpolated and extrapolated data set for the RCA.DAT data file ....... 151

45 Interpolated and extrapolated data for the Chatwin parameter for RCA.DAT

data file ........ ........... ........... ........ 152

46 Example of a sample ti me-concentrati on file to be converted . ........ 156

47 Example of a converted sample ti me-concentrati on file ... . ........ 157

48 Example of a measured sample ti me-concentrati on file .... . ........ 159

49 Example of a measured sample ti me-di scharge file ...... . ........ 162

50 Example of a converted sample ti me-concentrati on-di scharge file ....... 164

51 Plot of the Combi ne.out data ....... ........... ........ 169

x
PREFACE

The National Center for Environmental Assessment (NCEA) has prepared this document

for the benefit of EPA regional offices, States, and the general public because of the need to

develop a fast and easy method for evaluating tracer-breakthrough curves (BTCs) generated

from tracing studies conducted in hydrologic systems. Results may then be applied in solutetransport modeling and risk assessment studies.

The purpose of this document is to serve as a technical guide to various groups who

must address potential and/or existing contamination problems in hydrological systems.

Tracing studies are always appropriate and probably necessary, but analyses can be difficult

and tedious. This document and associated computer programs alleviate some of these

problems.

QTRACER2 is an update of the original QTRACER package (Field, 1999) which

was intentionally limited to fractured-rock and karstic aquifers. QTRACER2 addresses

hydrological-tracer tests conducted in all types of hydrological systems. These hydrological

systems include surface-water streams, granular aquifers, fractured-rock aquifers, and

subsurface-flow channels (e.g., mine tunnels, solution conduits, etc.). By necessity, some

hydrological systems are more amenable to certain types of analyses than are other

hydrological systems for the given information. For example, granular aquifers are not

amenable to head-loss estimation without an estimate for hydraulic conductivity. Much of

the original discussion material contained in QTRACER has been retained here because of

the necessity of emphasizing the value of quantitative tracer tests in general and in karst

aquifers in particular.

Another improvement included in QTRACER2 is the ability to provide correct moment

analyses for pulse and continuous releases. The original QTRACER package was intentionally limited to impulse releases because it was believed that most if not all tracer tests

conducted in fractured-rock and karstic aquifers consist of impulse releases. However, because short-pulse releases are commonly employed in other systems and long-pulse releases

are sometimes employed, it was deemed appropriate to include analyses for these types of

releases. Continuous releases are much less commonly applied, but the analyses are the

same as for long-pulse releases.

The changes applied in QTRACER2 required modifications to the original input files

read by QTRACER. These changes are documented in this report. Also, to bring

R QTRACER2 up-to-date with current PC operating systems (e.g., Windows )it was 

xi
necessary to reformulate much of the computer graphics which resulted in a loss in some

functionality and an increase in others.

Lastly, minor bugs discovered in the original QTRACER package after publication have

been corrected in QTRACER2. While no guarantee that QTRACER2 is bug free can be

provided, every effort has been made to identify and eliminate any bugs that may exist.

xii
AUTHOR AND REVIEWERS

The National Center for Environmental Assessment within the U.S. Environmental Protection Agency’s Office of Research and Development was responsible for the preparation of

this document and provided overall direction and coordination during the production effort.

AUTHOR

Malcolm S. Field, Ph.D. National Center for Environmental Assessment

U.S. Environmental Protection Agency

Washington, D.C.

REVIEWERS

C. Warren Campbell, Ph.D., P.E.

City Hydrologist

Engineering Department

City of Huntsville

P.O. Box 308

Huntsville, Ala.

Gareth J. Davies, P.G.

Principal Hydrologist

Cambrian Ground Water Co.

109 Dixie Lane

Oak Ridge, Tenn.

Clifford L. Ng

Environmental Engineer

U.S. Environmental Protection Agency

Region II

290 Broadway

New York, N.Y.

Robert B. Ambrose, Jr., P.E. U.S. Environmental Protection Agency

ORD/NERL/ERD-Athens

960 College Station Road

Athens, Ga.

xiii
ABSTRACT

Tracer testing is generally regarded as the most reliable and efficient method of gathering

surface and subsurface hydraulic information. This is especially true for karstic and

fractured-rock aquifers. Qualitative tracing tests have been conventionally employed in

most karst sites in the United States. Quantitative tracing tests are employed sparingly at

karstic sites in the United States, although it is widely recognized that they provide a wealth

of hydraulic and geometric data and are commonly employed in nonkarstic hydrological

systems. Quantitative tracer tests are regarded as more difficult and time-consuming than

qualitative tracing tests, which is a fallacy that needs to be overcome. The benefits of

quantitative tracing far outweigh any additional expenses incurred for all hydrologic systems.

An efficient, reliable, and easy-to-use computer program, QTRACER2, designed to run

R on PCs running any version of Microsoft Windows, has been developed to facilitate tracerbreakthrough curve (BTC) analysis. It solves the necessary equations from user-generated

data input files using robust integration routines and relies on established hydraulic models.

Additional features include dynamic memory allocation, the ability to extrapolate late-time

data using any one of three different methods, two separate methods for handling oversized

time-concentration data files, and a powerful interactive graphics routine.

Four other programs are included to facilitate the use of QTRACER2. The first,

NDATA, allows users to interpolate either their time-concentration or time-discharge data

files to fill in data gaps. The second program, AUTOTIME, allows users to convert timeconcentration data files recorded using military time (a 24-hour clock) into sequential

decimal time as required by QTRACER2. Files created by these two programs may be

combined and appended to the bottom of a sampling station data file that can then be read

by QTRACER2.

The easiest method for creating a new data-input file for use in QTRACER2 is to modify

an existing data-input file using a standard text editor (e.g., Notepad) and save the revised

file with a new name. However, if desired the user may access the third additional program,

DATFILE, to create or modify a data-input file by answering a series of querries posed by

the program.

Lastly, the fourth program was designed to address the problem of non-matching timeconcentration and time-discharge data. The program, COMBINE, combines two disparate

time-data sets into one time-concentration-discharge data set for use by Qtracer2.

xiv
1. INTRODUCTION

Quantitative tracing studies in hydrological systems are studies designed to provide detailed

information regarding flow dynamics. Such flow dynamics information generally cannot be

obtained from qualitative ground-water tracing studies (commonly employed in karstic solution conduits), although some aspects are often inferred (Smart et al., 1986). Quantitative

tracing studies consist of nothing more than the development of a tracer budget, i.e., comparing the amount of tracer injected into the aquifer system with the amount of tracer

recovered over time in conjunction with ground-water discharge measurements.

1.1. LIMITATIONS OF THIS REPORT

QTRACER2 was written to be as comprehensive as possible. However, as with any report

of this nature, it is necessarily limited in several areas. For example, one limitation that

will be obvious to modelers is the nonincorporation of solute-transport theory in the form of

transport equations. QTRACER2 was intended for tracer test analysis using the method of

moments the results of which can then be used in any number of solute-transport equations

in either the direct or inverse modes. Other more basic limitations are also evident in this

report.

1.1.1. Limitations Related to Type of Tracer

Although this report is intended to be generic in terms of tracer materials used, much

of the report will focus on the use of fluorescent-tracer dyes because of their inherent

desirabilities (Field et al., 1995). Field and Mushrush (1994) also established the value

of tracing petroleum-contaminated ground water using the common tracer dye fluorescein.

The numerical methods described herein, and the accompanying computer programs are

not tracer specific and may be used with any type of tracer material, provided it does

not degrade or decay. For example, the analyses described do not account for the specific

radioactive decay that will occur with radioactive tracers.

1.1.2. Types of Applicable Hydrological Systems

While most of this report focuses on tracing karst aquifers to define environmental problems,

other hydrological systems are also considered. Karstic aquifers are commonly considered to

be the aquifers most in need of tracing studies. Many professional hydrologists are beginning

to realize, however, that fractured-rock aquifers are just as much in need of tracing studies

1
as are karstic aquifers, but in general, tracing fractured-rock aquifers still receives minimal

acceptance beyond basic research projects. Assessments of surface-water streams, granular

aquifers, and other hydrological systems (e.g., glacial-outwash streams, mine shafts, etc.)

also benefit from tracing studies.

1.1.3. Quantitative Versus Qualitative Tracer Tests

Many aspects of quantitative tracing studies are no different than those of qualitative tracing

studies. The main difference is the level of information desired. The studies by Gaspar

(1987a,b), Mull et al. (1988), and K ̈aß(1998) contain discussions regarding tracer tests.

Readers must decide for themselves if a qualitative tracing test is sufficient or if a the

more detailed quantitative tracing test will better meet their needs. It is the opinion of

the author, and many other tracing professionals, that qualitative tracer tests (and/or the

ridiculous term, semi-quantitative tracer tests) are no longer acceptable and should never

be considered in lieu of quantitative tracer tests.

In those instances where field techniques applicable to quantitative tracing vary from

those applicable to qualitative tracing, an appropriate discussion will ensue. The reader may

want to note that the major difference between quantitative and qualitative tracing studies

is mostly one of mathematical analysis and interpretation based on a more comprehensive

tracer-sampling program, although tracer-injection methodology is also important.

1.1.4. Limitations Based on Test Design

Finally, it is important to note that QTRACER2 (and its predecessor, QTRACER [Field,

1999]) is intended for evaluating the results of tracer tests already conducted. QTRACER2

is wholly dependent on the quality of the data developed during the tracer test, which

requires good tracer-test design and implementation prior to analysis. This report does

not attempt to address either the design or implementation aspects of a tracer test. For

a comprehensive discussion and applicable methodology of tracer-test design, the reader is

referred to Field (2002a,b,c,d). For discussions regarding tracer-test implementation, the

reader should examine several of the references listed at the end of this report.

1.2. PURPOSE

A decision to conduct quantitative tracing studies is based primarily on the need to know

specific attributes of the aquifer being studied or monitored. For example, because of

2
the complexity of ground-water flow in karstic and fractured-rock aquifers, ground-water

monitoring can be extremely difficult. The main purpose of this document is to illustrate

the advantages of conducting quantitative tracing tests and to introduce the computer

program, QTRACER2 for tracer-breakthrough curve (BTC) analysis.

QTRACER2 is an efficient, reliable, and easy-to-use computer program designed to run

R on PCs running any version of Microsoft Windows. It was developed to facilitate BTC

analysis. QTRACER2 solves the necessary equations from user-generated data input files

using robust integration routines and by relying on established hydraulic models. Additional

features include dynamic memory allocation, ability to extrapolate late-time data using

any one of three different methods, two separate methods for handling oversized timeconcentration data files, and a powerful graphics routine.

1.2.1. Quantitative Tracer Tests to Support Ground-Water Monitoring Efforts

Qualitative ground-water tracing may establish a positive connection between a contamination source (Figure 1) and the monitoring locations, but probably will not provide sufficient

evidence as to whether or how much leachate may be escaping past the monitoring points.

Quantitative ground-water tracing provides a measure for determining the effectiveness of

the monitoring system by estimating the tracer loss involved. Inadequate tracer recoveries are an indication that losses other than sorption or decay (e.g., tracer migration to

unmonitored locations) may be significant.

1.2.2. Quantitative Tracer Tests for Risk Assessments

When dealing with hazardous-waste sites (e.g., Superfund sites), proof of the adequacy of

the existing or slightly modified ground-water monitoring system may be insufficient when

evaluating the risk posed by the site. A site risk analysis requires a complete description

of the release of the risk agent, its fate and transport in ground water and/or the vadose

zone, and any associated human and ecological exposure. To this end, it is necessary that

all contaminant-source areas and types of sources be identified, that the actual time of

travel of contaminants to all downgradient receptors be established, and that downgradient

concentrations be properly quantified. Quantitative tracing studies are an essential part of

any risk assessment of hazardous sites (especially in karstic and fractured-rock terranes),

because such studies provide much of the necessary information that otherwise could not

be obtained (Field and Nash, 1997; Field, 1997).

3
Figure 1. Contaminant leakage from a pesticide storage warehouse into a sinkhole located

in Manati, Puerto Rico. Pollutant stream is yellow in color and black sludge is built up

from past releases.

4
1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation

In some instances, it may be desirable to model the hydrologic system using theoretically

based solute-transport models. To calibrate these models to run in the direct mode (timeconcentration estimates), good parameter estimates are essential. Hydraulic and geometric

parameter estimates are most reliably obtained from tracer tests (Field and Nash, 1997).

Theoretically-based models that are run in the inverse mode (parameter optimization) can

and should be used to calibrate the parameters estimated from quantitative tracer tests

prior to evaluating contaminant migration by modeling solute transport in the direct mode

(Ma�loszewski, pers. comm.).

Field (1997) used parameters estimated from a quantitative tracing test in a solutetransport model (TOXI5) to effectively calibrate the model for use in estimating the fate

and transport of a hypothetical release of ethyl benzene. The model was run in the direct

mode to produce estimated ethyl benzene concentrations at a downgradient spring used for

drinking water.

Field and Pinsky (2000) used a theoretical two-region nonequilibrium model to optimize

parameters estimated from a series of tracer tests, to demonstrate the effect of immobileflow zones (dead zones) on solute migration. Parameter estimation, using the advectiondispersion equation, the two-region model, or even a three-region model, requires that

reasonably reliable parameter estimates be employed so that a global minimum can be

found during optimization.

1.3. QUALITATIVE VERSUS QUANTITATIVE TRACING

Many well-head protection studies and landfill investigations/monitoring may be adequately

addressed by qualitative tracing studies. Recharge/discharge areas are routinely established

from successful qualitative dye-tracing studies and are commonly used to establish simple

classes of conduit networks (Atkinson et al., 1973; Brown, 1973; Smart, 1988a). Qualitative

dye-tracing studies are often used to estimate apparent pollutant transport rates from

apparent tracer velocities. Given the potential for additional costs and labor associated

with conducting and interpreting quantitative tracing studies, qualitative tracing studies are

often considered appropriate, but this may not be the case. In other instances, additional

details of the aquifer under investigation need to be established.

It has been suggested that quantitative tracing studies are too expensive because (1)

required sampling at a frequency sufficient to yield reliable results, and (2) the many possible

5
places the tracer might go, both situations requiring frequent sample collection at tens or

even hundreds of locations. Neither of these objections are valid.

With the advent of low-cost programmable automatic water samplers, continuous flowthrough filter fluorometers (Figure 2), and recently developed fiber-optic fluorometers

(Barczewski and Marshall, 1992; Benischke and Leitner, 1992) and spectrophotometers,

adequate sampling frequencies are easily established. The only difficulty is the necessary

power requirements, but automatic water samplers do not draw very much power and can

be run on battery power for long periods.

Figure 2. A Turner DesignsR Model 10AU field filter fluorometer operating in the flowthrough mode at Pearl Harbor Naval Base. The red valve is set horizontally to allow inflow

of water from the bottom connector and discharge out the top connector.

Quantitative tracing studies have proved that a generalized estimate for ground-water

flow direction(s), based on potentiometric-surface maps, geological structure, and geological

6
stratigraphy, can be developed. Therefore, tracing experts can provide a reasonably good

guess where tracers may be recovered without having to sample “everywhere,” as has been

advocated in the past. In addition, a “...well-designed tracer test, properly conducted, and

correctly interpreted...” (paraphrased from James F. Quinlan) is likely to provide sufficient

information for a determination as to whether tracer migration to unmonitored locations

has occurred.

Quantitative tracing studies can be more valuable than qualitative tracing studies

for answering specific questions. Quantitative tracing studies are often conducted after

qualitative tracing studies have adequately established the ground-water flow trajectories

and apparent ground-water flow velocities so that costs and labor efforts may be minimized.

Ground-water problems, such as pollution migration from hazardous-waste landfills, often

demand more sophisticated quantitative ground-water tracing studies because of the need

to better define subsurface hydraulic processes. Quantitative tracing studies can also

provide significantly better insights into the functioning of the hydrological system than

qualitative tracing tracing studies. Reliable estimates for tracer mass recovery, mean

residence times, mean ground-water flow velocities, longitudinal dispersion, and maximum

volume contact by the tracer allow for useful evaluations of the hydraulic processes of

dispersion, divergence, convergence, dilution, and storage (Atkinson et al. 1973; Smart,

1988a; Field and Nash, 1997). Such improvements in karst aquifer evaluation efforts

translate into better ground-water resource management, ground-water monitoring designs,

and ground-water remediation (Smart, 1985).

Finally, it must be noted that qualitative tracing studies can lead to serious misinterpretations regarding aquifer connections. Smart et al. (1986) compared the results of

qualitative and quantitative tracing for the Traligill Basin in Scotland and determined that

the qualitative tracing results did not properly establish the subsurface connections.

7
2. TRACER TEST DESIGN FACTORS

Conducting quantitative-tracing studies requires considerable knowledge of the tracer type

employed. Simple measurement errors may occur as a result of tracer-specific effects,

inappropriate sampling, and/or inappropriate analysis (Smart, 1988a). Smart and Laidlaw

(1977), as well as other sections of this document, discuss specific attributes of many of the

fluorescent dyes commonly used for tracing ground-water flow. Field et al. (1995) provide a

comprehensive discussion of the toxicity characteristics of several fluorescent dyes commonly

used for tracing studies. Some typical fluorescent dyes used for tracing are listed in Table 1

and their structures shown in Figure 3.

Table 1. Some commonly used fluorescent dye types, their dye names, and their respective

Colour Index and CAS numbers.

Dye Type and Colour Index CAS No.

Common Name Generic Name

Xanthenes 

sodium fluorescein

eosin

Rhodamines 

Rhodamine B

Rhodamine WT

Sulpho Rhodamine G

Sulpho Rhodamine B

Stilbenes 

Tinopal CBS-X

Tinopal 5BM GX

Phorwite BBH Pure

Diphenyl Brilliant Flavine 7GFF

Functionalized Polycyclic 

Aromatic Hydrocarbons 

Lissamine Flavine FF

pyranine

amino G acid

Acid Yellow 73 518-47-8

Acid Red 87 17372-87-1

Basic Violet 10 81-88-9

Acid Red 388 37299-86-8

Acid Red 50 5873-16-5

Acid Red 52 3520-42-1

Fluorescent Brightener 351 54351-85-8

Fluorescent Brightener 22 12224-01-0

Fluorescent Brightener 28 4404-43-7

Direct Yellow 96 61725-08-4

Acid Yellow 7 2391-30-2

Solvent Green 7 6358-69-6

— 86-65-7

Appropriate sampling efforts and frequencies for both tracer dye and discharge exert

considerable influence on the accuracy of quantitative dye-tracing studies. Analytical

8
Figure 3. Chemical structures for selected fluorescent dyes used for water tracing.

9
methods must yield results with a high degree of precision as well. The fluorescent dyes

listed in Table 1 fluoresce in the visible light spectrum anywhere from about 435 nm

(Tinopal CBS-X) to approximately 584 nm (Sulpho Rhodamine B) (Table 2) (Figure 4).

Table 2. Data on some common fluorescent tracer dyes.

Dye Name Maximum Maximum Fluorescence Detection Sorption

Excitation λ Emission1 λ Intensity Limit2 Tendency

(nm) (nm) (%) (μg L−1)

sodium fluorescein

eosin

Rhodamine B

Rhodamine WT

Sulpho Rhodamine G

Sulpho Rhodamine B

Tinopal CBS-X

Phorwite BBH Pure

Diphenyl Brilliant

Flavine 7GFF

Lissamine Flavine FF

pyranine

amino G acid

sodium napthionate

492 513 100 0.002 very low

515 535 18 0.01 low

555 582 60 0.006 strong

558 583 25 0.006 moderate

535 555 14 0.005 moderate

560 584 30 0.007 moderate

355 435 60 0.01 moderate

349 439 2 ? ?

415 489 ? ? ?

422 512 1.6 ? ?

4603 512 18 ? ?

4074 512 6 ? ?

359 459 1.0 ? ?

325 420 18 0.07 low

1. Values are approximate only. Different instruments will yield slightly different results.

2. Typical values for tracer detection in clean water using spectrofluorometric instrumentation.

Values may be adversely affected by augmented fluorescence and/or scattered light background.

Values will be lower when using filter fluorometric instrumentation.

3. pH ≥ 10

4. pH ≤ 4.5

Source: Behrens, 1986., Worthington, pers. comm.

Tracer tests in karstic and fractured-rock aquifers may be additionally affected by unknown

subsurface pathways. Different types of solution-conduit and fracture-flow networks will

have a significant effect on tracer mass recovery, but this may be unknown to the tracing

professional. These factors can be problematic when interpreting either qualitative- or

quantitative-tracing study results and cannot be ignored.

10
Figure 4. Electromagnetic spectrum with enlargement of visible spectrum for tracer dyes.

Modified from Wilson et al. (1986, p. 3).

2.1. TRACER CHARACTERISTICS

All chosen tracer substances should exhibit certain “ideal” characteristics, most notably

conservative behavior. Unfortunately, no tracer substance is ideal, but fluorescent dyes

are appropriate for tracing hydrologic systems because of their low purchase cost, ease of

use (injection, sampling, and analysis), low toxicity, relatively conservative behavior, high

degree of accuracy of analysis, and low cost of analysis. However, specific aspects of any

particular tracer dye chosen for a tracing study may adversely affect tracer recovery and

thus lead to incorrectly calculated results (e.g., mass-balance errors). For example, sodium

fluorescein (Acid Yellow 73) naturally photodecays, which is problematic for surface-water

tracer tests.

When conducting qualitative dye-tracing studies, it is usually sufficient to inject a known

quantity of dye on an “as sold” basis, which means that a considerable amount of diluent

has been added to the dye (i.e., < 100% dye). However, when conducting quantitative

dye-tracing studies, the actual mass of dye injected into the aquifer must be known if the

calculations are to be performed correctly.

Consider, for example, the commonly used fluorescent-tracer dye Rhodamine WT (Acid

11
Red 388). For a qualitative trace, the tracing professional may decide to inject 18 pounds (2

gallons on an as sold basis) into the aquifer and be satisfied with the outcome. A quantitative

trace would, however, require that the actual mass of the dye injected be calculated because

Rhodamine WT is sold as a 20% solution (actually, it is sold as a 17.5% solution, but is

listed as a 20% solution) and because it has a density of 1.19 g cm−3. In this particular

instance, the conversion to mass is developed from the following formula (Mull et al., 1988,

p. 61):

V × ρ × % = Min (1)

where V isvolume [cm3], ρ is density [g cm−3], % is purity, and Mi is mass injected [g].

To determine the actual dye mass injected into the aquifer, the user must perform the

following calculations:

1. Convert gallons to equivalent SI units (cubic centimeters for this example)

2.0 gal × 3.785 × 10−3 = 7.570 × 103 cm3

where 3.785 × 10−3 is a conversion factor.

2. Next insert the value obtained in step 1 into Equation (1)

7.570 × 103 cm3 × 1.19 g cm−3 × 1.75 × 10−1 = 1.61 × 103 g

= 1.61 kg

Subsequent quantification calculations would then use 1.61 kg for the mass of dye injected

into the aquifer. Similar calculations for other tracer types need to be made using tracerspecific information.

Tracer sampling also presents some difficulty, depending upon the behavior of the tracer.

All tracers will exhibit some loss due to sorption onto aquifer materials, but other factors

may also cause a loss of tracer mass in the samples. For example, the commonly used tracer

dye, sodium fluorescein (Acid Yellow 73), tends to photodecay so that excess exposure

to sunlight may diminish total mass recovery. Rhodamine WT is temperature dependent

and requires correction of field measurements to a standard temperature. Even worse, it

has recently been shown that Rhodamine WT naturally degrades to carboxylic fluorescein,

which may substantially interfere with analyses and interpretations if sodium fluorescein

12
was also used during the study (Gareth Davies, pers. comm.). Pyranine (Solvent Green

7) is pH dependent, which requires careful buffering of the water samples prior to analysis

(Smart and Laidlaw, 1977).

2.2. TRACER INJECTION

Ground-water and surface-water tracing both require labeling or “tagging” the flowing water

with some identifying substance (i.e., tracer) for subsequent detection at some distant point.

This can be achieved only by getting the tracer to mix with the water. For surface-water

tracing, this is not difficult. However, labeling ground water with a tracer can be a fairly

involved process.

Typically, for karst systems the tracer substance, usually a fluorescent dye, is injected

directly into a sinkhole or sinking stream that is believed to be connected to the solutionconduit system. Figure 5 depicts a reinforced sinkhole located at the RCA del Caribe

Facility (Barceloneta, Puerto Rico) that was used for plant waste-water injection and for

tracer injection. Although small in appearance, this is a substantial entry point for water

and pollutants.

Boreholes and wells are often used as injection points, but these are not as effective

as sinkholes and sinking streams. Sinkholes and sinking streams are directly connected to

the subsurface “plumbing” system of a karstic aquifer. Boreholes and wells, in general, are

rarely connected to the subsurface flow system.

Once injected, the tracer will move through the hydrological system. Figure 6 depicts

a fairly typical solution conduit that may exist in an area. From Figure 6 it is obvious

that if the conduit shown was at a depth of approximately 10 to 30 meters, it would be

nearly impossible to detect it by any known geophysical means, or to intersect it by a well.

Monitoring wells are next to useless in this instance. However, a slug of tracer dye would

use this conduit to migrate to a point where detection is possible.

2.2.1. Methods of Injection

Tracer injection can be achieved using a variety of methods. For example, it is not atypical to

observe an injection in which a powder or liquid dye is injected (“dumped” and “introduced”

are synonyms) directly into a sinkhole, sinking stream, or monitoring well. However, it

is usually desirable to mix powder tracers with water prior to injection to prevent site

contamination by air currents. The tracer/water mixture is then more easily poured into

the injection point. Powder tracer mixing is most easily accomplished by adding a measured

13
Figure 5. Reinforced sinkhole receiving plant waste water at the RCA del Caribe Facility.

Waste water appears as clear water discharging from the rust colored pipe inside the

sinkhole.

quantity of tracer into a large carboy (e.g., 5 L) containing a small quantity of water

(Figure 7).

After the preferred amount of tracer has been added to the carboy, more water is added to

the mixture to bring the level up to about one-half to one-third full. The cap is then screwed

down tightly, and the carboy shaken vigorously to effect a thorough mixing. The carboy

should be weighed before and after all additions and after injection so that a reasonably

accurate estimate of tracer mass can be recorded. The contents of the carboy are then easily

released into the injection point (Figure 8).

Many of the commonly used fluorescent dyes that were previously available in powder

form are now available in liquid form. The liquid form of the powder dyes exhibit

greatly reduced concentrations when compared with the powder form (Table 3), but the

14
Figure 6. Dissolutionally enlarged fissure in limestone where most flow will occur. Precipitation of calcium carbonate in fractures appears as white and/or brown streaks.

concentration is insignificant when mass is used to determine the appropriate tracer mass.

Given the availability of liquid dyes there appears to be no useful or valid reason for using

the powder form.

Prior to tracer injection a substantial quantity of water (e.g., 1000 gal.) should be

released into the sinkhole or monitoring well (this is unnecessary for sinking streams). This

“primer” of water helps to lubricate the system and to flush out any debris. The tracer may

then be added to the inflowing water. Alternatively, the water injection may be halted for

tracer injection and then restarted after tracer injection.

A large quantity of chaser water (e.g., 3000 gal.) is injected after tracer injection to

help move the tracer along. Chase water helps to prevent the tracer getting stored in large

dead-end pores and behind other obstructions. However, it is necessary in some instances

(e.g., monitoring wells) that care be taken not to raise the head excessively. Experience has

15
Figure 7. Mixing fluorescein powder dye with water in a 5 L carboy. Fluorescein is a

brick-red color when a dry powder.

16
Figure 8. Injecting mixture of water and fluorescein dye into an injection well. Fluorescein

has a dark red color when concentrated as shown here, but becomes a bright fluorescent

green when diluted.

17
Table 3. Percent pure dye content for selected fluorescent dyes.

Colour Index Powder Dye Liquid Dye Specific Gravity

Generic Name (%) (%) (g cm−3)

Acid Blue 9

Acid Red 52

Acid Red 87

Acid Red 388

Acid Yellow 73

Basic Violet 10

Fluorescent

Brightener 351

Solvent Green 7

74.0∗ 37.0 —

90-92.0 18.0 1.175

86.0 26.0 —

85.0∗∗ 17.0 1.160

60.0 30.0 1.190

90.0 45.0† —

60.0 — —

80.0 — —

Values listed are equal to within ±5.0%. ∗Acid Blue is also sold with a Food, Drug and Cosmetic (FD&C)

purity equal to 92.0%. ∗∗Acid Red 388 is not commercially available in powder form. †

Basic Violet 10 as a liquid is mixed with glacial acetic acid.

Note: The values listed are specific to one manufacturer; crude dye

stocks can and will vary significantly with manufacturer.

shown that a slow flow (e.g., ≤ 50 gpm) is more effective than a rapid flow.

2.3. TRACER SAMPLING

Sampling for tracer must be performed in conjunction with discharge measurements for

quantitative tracing because ground-water discharge and tracer-mass recovery are strongly

interconnected. If discharge is not measured during the tracing study, but water samples

are collected, then the tracing study may be considered semi-quantitative. Sampling must

also be of sufficient frequency to avoid the problem of aliasing (Smart, 1988a). Aliasing

occurs when sampling frequencies are inadequate (i.e., time intervals between individual

sampling events are too far apart), which may cause certain aspects of tracer recovery to

go unobserved.

Additionally, cessation of sampling prior to complete recovery of the tracer mass may

lead to an inadequate estimate of the aquifer characteristics desired. Field and Nash (1997)

demonstrated the efficiency of numerical interpolation/extrapolation algorithms to fill gaps

in the sampling-data record.

18
2.4. SAMPLING EQUIPMENT

Mull et al. (1988, pp. 38–39) recommend that samples be collected by automatic samplers

using glass sample bottles to minimize losses. Automatic samplers can be programmed to

collect a water sample at appropriate sampling frequencies so that even late-night samples

may be conveniently collected. Glass sample bottles are less likely to sorb the tracer than

are plastic sample bottles, which may distort sample-analysis results. Even if automatic

samplers are not to be used, glass sample bottles are still appropriate for sample collection.

The sample bottles need only be large enough to hold a maximum of approximately 32 mL

of water in most instances.

Grab samples using appropriately sized test tubes with caps (e.g., 25 mm × 150 mm)

minimize handling. Samples should be stored tightly capped in a cool, dark place. Shipping

to the laboratory should be by cooler, with an ice block enclosed.

Packets of activated charcoal may also be collected if fluorescent dyes are used as tracers.

It is believed that activated charcoal will ensure dye recovery because the supposed much

lower dye concentrations found in water samples may not be detected in the water, or

sampling frequencies may not have been adequate. The ability of activated charcoal to

continue sorbing and concentrating fluorescent dye provides a sound means for determining

fluorescent dye occurrence when water samples are ambiguous. However, at best, activated

charcoal will result in a qualitative tracing test only. More seriously, there is considerably

more opportunity for sample contamination from handling. Still more serious is the recently

considered problem of false positives and false negatives associated with activated charcoal

packets (Smart and Karunaratne, 2001; Smart and Simpson, 2001).

2.5. SAMPLING LOCATIONS AND FREQUENCIES

Sampling locations and frequencies can be based on the results of qualitative dye-tracing

studies so that appropriate sampling locations and frequencies may be determined before

conducting quantitative tracing studies. Preliminary qualitative tracing studies may

help ensure that proper sample collection will occur, while minimizing expenses when

quantitative tracing efforts are undertaken.

Should quantitative ground-water tracing efforts be initiated prior to qualitative tracing

efforts, it is possible that too many or too few sampling locations will be utilized; the

former drives up the cost, while the latter results in incomplete tracer mass recovery.

Sampling frequencies may also be inadequate, resulting in added costs (excessive number

19
of samples collected) or inadequate tracer mass recovery (too few samples collected too

infrequently). Preliminary simple ground-water tracing studies can be useful for more

difficult and complicated tracing studies. However, as previously discussed (Section 1.3.

on page 5), recent studies have proven that, with a basic understanding of the local

hydrogeology and the use of automatic water sampling equipment, qualitative tracing efforts

need not be conducted prior to quantitative tracing efforts.

2.6. TRACER MIXING IN THE FLOW SYSTEM

Complete lateral and vertical mixing of the tracer is considered ideal, but not always

possible. An acceptable mixing length is one in which the travel distance allows for nearly

complete lateral mixing of the tracer, and is considered to be an important factor in tracing

surface-water flows (Kilpatrick and Cobb, 1985, pp. 2–3). Unfortunately, ground-water

tracing does not always ensure that adequate lateral mixing will occur in solution conduits

or fractures because tracing efforts are constrained to the limits of tracer-injection points as

related to tracer-recovery points. Inadequate mixing may result in incorrect tracer-recovery

calculations.

Mull et al. (1988, pp. 43–44) recommend that sampling during preliminary traces occur

(at a minimum) at three places in the cross-section of the spring and the BTC plotted

for each sampling point in the cross-section. Complete lateral mixing is determined to

have occurred when the areas under the BTCs, for each sampling location, are the same

regardless of curve shape or magnitude of the peaks. Optimum results are obtained when

mixing is about 95% complete (Figure 9) (Kilpatrick and Cobb, 1985, p. 3).

2.7. CORRECTION FOR TIME TO REACH FLOW SYSTEM

For some tracer injections, accurate time of travel, velocity, and dispersion estimates require

that the time needed for the tracer to reach the flow system (e.g., infiltration time) be taken

into account for a more accurate estimate. Tracer flow velocity is adjusted for time to reach

and/or exit the flow system by subtracting tinf from the total real time of travel values ti

and integrating. However, this will lead to negative times of travel, so it is easier to subtract

tinf from the mean time of travel t

 ̄ to obtain the true tracer velocity (Dole, 1906, p. 78)

x

υ ̄ = (2) t

 ̄− tinf

20
Figure 9. Typical response curves observed laterally and at different distances downstream

from a slug injection of a tracer in the center of a stream where the symbols are defined in

the Notations section (page 172) (Kilpatrick and Cobb, 1985, p. 3).

The difference between the true velocity and the perceived velocity is then (Dole, 1906,

p. 78)

x tinf υ ̄ = (t

 ̄− tinf )t ̄ (3)

with a consequent correction for dispersion. While this adjustment is usually not necessary

for surface-water tracer tests and many tracer injections into disappearing streams and

sinkholes, it may be absolutely essential for accurate analyses for deep aquifers, or slow

infiltration through the beds of sinking streams.

2.8. CORRECTION FOR BACKGROUND

All field measurements need to be corrected by subtracting background tracer concentrations

from measured tracer concentrations. For example, sodium fluorescein is used to color

automobile antifreeze. Because there are so many automobiles in existence and so many of

them have leaks in their radiators, fluorescein-colored antifreeze is fairly ubiquitous in the

environment.

Prior to any tracing efforts, background water samples Cbi need to be collected and

analyzed for the tracer of interest. If the values obtained are low enough (e.g., few μg L−1),

21


then the chosen tracer may be used. If not, then a different tracer should be chosen. Low

background concentrations in samples will then need to be averaged Cb because it is not

possible to subtract a suite of background concentrations from the measured concentrations.

This final average background concentration is subtracted from every sample of recovered

tracer from subsequent tracing efforts

Cif = Cii − Cb (4)

where

Cb = 1

n

n

1

Cbi (5)

In addition, instrument calibration (e.g., scanning spectrofluorophotometer and filter

fluorometer) should be performed as described in the appropriate U.S. Geological Survey

Techniques of Water-Resources Investigations publications (Kilpatrick and Cobb, 1985;

Wilson et al., 1986). Proper instrument calibration is essential. Calibration using distilled

water is common, but use of sample water is also acceptable.

2.9. DISCHARGE MEASUREMENTS

As stated previously, tracer sampling must be performed in conjunction with discharge

measurements. If sampling is performed at wells that are being pumped at a constant rate,

then discharge is fairly easily determined. Discharge at springs is considerably more difficult

to estimate. If grab samples are being collected from non-pumping wells, then some estimate

for flux past the well may need to be established.

Estimation of discharge may require special efforts on the part of the tracing professional.

Weirs may need to be built, standpipes installed, flow meters utilized, and losses to

evaporation estimated (for large bodies of water). Numerous documents describing methods

for estimating discharge already exist so the techniques will not be discussed here. Interested

readers should examine the appropriate U.S. Geological Survey Techniques of WaterResources Investigations publications for comprehensive discussion of discharge estimates.

Important to note is the possible occurrence of transient high-level overflows in which

normally dry springs may discharge large quantities of water during storm events. Springs

that are normally dry during low- to moderate-flow conditions may function during highflow conditions. Efforts to address irregularly functioning springs should be prepared prior

to initiating quantitative-tracing studies so that discharge of tracer at such springs can be

recovered.

22
Less common is the problem of sampling well screens set at elevations below which

high-flow conditions occur. Such wells may be adequate for recovering tracer during lowand moderate-flow conditions, but incapable of drawing in and discharging tracer during

high-flow conditions. Presumably, such an occurrence would be addressed by appropriate

sampling at downgradient high-flow springs.

2.10. KARST CONDUIT NETWORKS

Tracing studies used in the determination of subsurface flow conditions in karst terranes are

greatly influenced by various combinations of subsurface flow networks located between the

inflow and outflow points of the aquifer. Seven types of karst networks are known to exist,

as schematically shown on Figure 10.

The influence of karst networks on tracer quantity present at a recovery site can be

significant. If flow is through the simple Type I network, dye quantity estimates may be

reasonably accurate. The more complex the karst network, however, the less likely it is that

estimates of dye quantity will be adequate. As estimates become more difficult to make, it

becomes tempting to use more dye than necessary. For Types II through VII (but excluding

Type V), the estimate of dye quantity is likely to be low.

2.10.1. Network Types I, II, and III

If flow is through a Type I network, then predictions based on common tracing techniques

may be reasonably accurate. If flow is through a Type II or Type III network, the accuracy

of the predictions will tend to be inversely proportional to the amount of dye that is either

diluted by additional water inflow or diverted to unknown discharge points. Distributary

flow and multidirectional flow are subtypes of Types III and IV.

2.10.2. Network Types IV and V

Types IVa and IVb further complicate the flow determination because of significant loss

of dye and because the identified outflow point will have a discharge rate that may be less

than, greater than, or equal to the inflow point. Type V presents the worst situation related

to flow prediction because no dye is recovered. This can lead to a false conclusion of a lack

of hydraulic connectivity (i.e., if the dye goes elsewhere, such results indicate there is no

flow to the sites being monitored).

23
Figure 10. Seven simple karst network types that describe tracer migration in karst conduits.

Any of these networks may significantly influence tracer tests between the point of inflow

(IN) and the point of outflow (OUT) in a karst system. Discharge into the conduit is q,

discharge out of the conduit is Q, tracer mass injected into the conduit is mi, and tracer

mass recovered is TT . Note: Any one of these network types may be interconnected with

any of the others. Modified from Atkinson et al. (1973) and Gaspar (1987b, p. 64).

24
2.10.3. Network Types VI and VII

Types VI and VII are situations where either a significant amount of ground-water storage

exists or a separate karst subsystem is connected to the main karst system. These are really

subgroups of any one of Network Types I, II, III, IV, or V. As drawn, Network Types VI

and VII appear only as subgroups of Network Type I, but additional inflows, outflows, or

no connection to the sample-collection station(s) are realistic possibilities. For contaminant

transport in a karst system, Network Types VI and VII may play significant roles.

2.11. DETERMINATION OF TOPOLOGICAL KARST CONDUIT NETWORK TYPE

Determination of the karst conduit network type usually requires extensive cave exploration,

but can be roughly estimated from quantitative ground-water tracing studies. This is

achieved by recognizing that each topological type exhibits specific characteristics that

influence the results of tracing studies (Atkinson et al., 1973).

A Type I network (Figure 10) will exhibit such characteristics as inflow discharge equal

to outflow discharge and mass of injected tracer equal to mass of recovered tracer

q = Q

Min = Mout

This assessment seems intuitively obvious considering that, for both the inflow and

outflow discharges to be equal and for complete tracer recovery to occur, requires that a

simple straight tube be defined. Other topological types become more difficult to assess as

discharges and tracer recoveries become more complex (Figure 10).

It will be noted that Network Types VI and VII may fit into any one of the above

categories, but with the added effect of storage in the system. Storage is not, however,

accounted for in the simple relationships because it is only a delaying mechanism.

25
3. QUANTITATIVE TRACING METHODOLOGY

Quantitative tracing studies are based on a detailed study of BTCs, which are generated

from quantitative chemical analyses (e.g., fluorescence) of a series of water samples, in

combination with ground-water discharge measurements for each sampling station at which

tracer was recovered. Tracer-breakthrough curve shape for hydrological systems depends

upon:

• Character of the tracer;

• Prevailing flow conditions;

• Structure of the aquifer (Smart, 1988a);

Discussion of these conditions, as related to BTCs, has already been addressed and reviewed

by Smart (1988a). Successful quantitative ground-water tracing studies are dependent upon:

• Conservative behavior of the tracer substance;

• Precise instrument calibration;

• Adequate quantity of tracer substance to be injected;

• Sufficient monitoring frequency at all downgradient receptors;

• Precise discharge measurements at downgradient receptors; and

• Sufficient length of monitoring period for total tracer mass recovery.

These factors may be achieved through good design, implementation, and persistence.

Various problems tend to arise when the above factors are not considered in the design of

a tracing study. Such problems may include no tracer recovery, incomplete tracer recovery,

or aliasing of the BTC (Smart, 1988a). These problems lead to fundamental questions

regarding the tracing study. If none or only some of the injected tracer mass was recovered,

what caused incomplete recovery? What was the mean residence time (mean tracer transit

time) for the tracer in the aquifer? What were the mean and apparent tracer velocities

assuming advection only? How significant was longitudinal dispersion in the aquifer?

In terms of contaminant transport, answers to these questions are essential. Some of

the questions can be answered by only making best professional interpretations of the BTC.

26
Figure 11. Definition sketch of BTCs along a selected tracer streamline from an instantaneous tracer injection (Kilpatrick and Wilson, 1989, p. 3).

Others may be answered by careful numerical analysis of the BTC. For example, in instances

of insufficient sampling frequency or cessation of sampling prior to total tracer mass recovery,

good interpolation/extrapolation algorithms may be used to fill gaps in the data. However,

problems of aliasing may not be addressed by such efforts while extrapolation of data beyond

real sampling times may not provide realistic values.

3.1. ESTIMATION OF HYDRAULIC PARAMETERS

Hydraulic parameters may be estimated by the method of moments. The zeroth moment

is used to estimate the tracer mass recovery. The first moment is used to estimate the

mean residence time and mean flow velocity. The second moment is used to estimate the

longitudinal dispersion. However, as will be shown, the second moment may not provide

reliable estimates for dispersion (Field and Pinsky, 2000).

Analysis by the method of moments is nothing more than determining the area under

the BTC generated by plotting time versus measured tracer concentrations (Figure 11).

The following discussion is taken from Kilpatrick and Wilson (1989, p. 3 and 4).

The BTCs along a streamline shown in Figure 11 may be described in terms of elapsed

27
time after a slug injection. Characteristics pertinent to the BTC analysis are:

• TL, elapsed time to the arrival of the leading edge of the BTC at a sampling point;

• Tp, elapsed time to the peak concentration Cp of the BTC at a point;

• Tc, elapsed time to the centroid of the BTC at a point; and

• Tt, elapsed time to the trailing edge of the response curve at a point.

The mean travel time for the flow along a streamline is the difference in elapsed time of

the centroids of the BTCs defined upstream and downstream on the same streamline given

by

tc = Tcn+1 − Tcn (6)

where n is the number of the sampling site. Similarly, the travel times of the leading edge,

peak concentration, and trailing edge along a given streamline are, respectively

tL = TLn+1 − TLn (7)

tp = TPn+1 − Tpn (8)

and

tt = Ttn+1 − Ttn (9)

The time Td necessary for the tracer mass to pass a sampling point in a section is

Td = Ttn − TLn (10)

As shown in Figure 11, a typical tracer cloud may travel faster in the center of the stream

than along the flow channel walls, where it may also be elongated. Complete definition of

the BTC may involve measurement at more than one point or streamline at several sections

(if possible). Usually, in hydrologic systems other than surface streams, such elaborate

sampling is not possible. Samples are acquired where feasible. It also may not be necessary

if adequate mixing has occurred. However, it is advisable to sample at least three points

along a cross section of a spring, if possible, to ensure adequate mixing.

The duration or time of passage of a tracer response at a section TD is the difference

between the slowest trailing time along a flow channel and the fastest leading edge time,

28


usually observed in the center. The difference between the values of Td and TD can be

significant. It is usually assumed that TD ≈ Td.

The remainder of this document will not rely on Equations (6)–(10) because it is rare for

ground-water tracing studies to provide an opportunity for sampling at multiple locations

along a streamline. Direct access to a cave during a tracer test is one exception.

3.1.1. Total Tracer Recovery

Estimation of tracer recovery for individual sampling stations is given by Equation (11)

(modified from Gaspar, 1987b, p. 62)

∞

MO = C(t) Q(t) dt (11)

0

and total tracer recovery from all downgradient receptors may be estimated from Equation (12) (Gaspar, 1987b, p. 63)

n

MT = MOi (12)

i=1

These models assume complete mixing of the tracer substance with water, negligible

dispersion effects, and that the tracer mass will ultimately exit the aquifer system completely

at one or more downgradient receptors as a function of time and discharge.

A simple total mass recovery equation for a single sampling station was developed by

Mull et al. (1988, p. 52) that includes a necessary unit conversion factor, because English

and SI units are intermixed in their equation. Other than the necessary unit conversion

factor, this equation yields acceptable results if proper care is taken in the execution of the

tracing study. Their equation is not reproduced here to avoid confusion with Equation (11)

of this section.

3.2. QUALITY OF TRACER MASS RECOVERY

The quality of the tracer experiment may be quantified in terms of mass recovered. Usually,

the quality of the tracer experiment is given as a percent of mass recovered, but this affords

little insight. An accuracy index given by Sukhodolov et al. (1997)

Min − MT AI = (13) Min

provides more insight into the quality of the tracing experiment. An AI = 0 indicates a

perfect tracing experiment. A positive AI indicates more mass injected than was recovered,

29
while a negative AI suggests more mass recovered than was injected. As AI moves further

away from zero, the quality of the tracing experiment gets poorer.

A high degree of precision for tracer recovery has considerable utility. For evaluation of

ground-water monitoring and contaminant transport, total tracer mass recovery is essential.

Tracer mass recovery should be quantified to ensure that all relevant locations are properly

monitored for ground-water quality. Otherwise, it is likely that important ground-water

discharge locations may be missed. A low-percent recovery of a conservative tracer mass

may be an indication of significant loss of tracer during the study, often a result of improper

determination of downgradient receptors. A high-percent recovery is a probable indication

that most, if not all, relevant downgradient receptors were properly monitored for tracer

recovery. For contaminated sites of a controversial nature (e.g., Superfund sites), this can

be critical.

3.2.1. Mean Residence Time

Mean tracer residence time is the length of time required for the centroid (gravity mass) of

the tracer to traverse the entire length of the aquifer system, representing the turnover time

for the aquifer. The centroid is generally not the same as the peak concentration of the

tracer in the BTC, but the more flow conforms to Fick’s law, the less obvious the difference

between the centroid and the peak concentration.

Mean tracer residence time for impulse and short-pulse releases (t2 < t

 ̄)isesti mated

from Equation (14) (modified from Gaspar, 1987a, p. 93)

∞

t C(t) Q(t) dt

 ̄ 0 t = ∞ (14)

C(t) Q(t) dt

0

and for long-pulse and continuous releases (t2 ≥ t

 ̄) from (Sardin et al., 1991)

∞

t

 ̄= [1 − F(t)] dt (15)

0

where

C(t) F(t) = (16) Cp

Travel-time variance for impulse and short-pulse releases (t2 < t

 ̄) is estimated from

30
Equation (17) (modified from Mull et al., 1988, p. 58)

∞

(t − t

 ̄)

2 C(t) Q(t) dt

σt

2 = 0

∞ (17)

C(t) Q(t) dt

0

and for long-pulse and continuous releases (t2 ≥ t

 ̄) from (Sardin et al., 1991)

∞

σt

2 = 2 [1 − F(t)]t dt − t

 ̄2 (18)

0

It will be noted that for Equations (17) and (18) to be appropriate for long-pulse releases, the

time-concentration data file must be truncated so that the descending time-concentration

data is ignored in the calculations.

Equations (14) to (18) assume that tracer residence time will vary from zero for

instantaneous exit of the tracer mass from the aquifer system to infinity for tracer mass

that is stored in micropores. They provide relevant information on the time required for the

centroid of a nonreactive pollutant mass spilled in the vicinity of the injected tracer mass

to reach a downgradient receptor.

Mean tracer residence time may be estimated by summation algorithms, a simplified

version of which was developed by Mull et al. (1988, p. 56). Their equation provides

good results, but may be confusing to the uninitiated, and may also be confused with

Equation (14). A simplified example calculation is performed later in this report (see

Section 4. on page 48).

A method for estimating mean tracer residence time was also developed by Smart

(1988b) using time-concentration integrals that are based on a routine in Church (1974).

This method does not include discharge in the calculation, but is generally similar to that

presented in this section. This method has not been tested by this author but may be

regarded as acceptable.

For contamination studies, initial tracer breakthrough (i.e., first arrival) may be considered more valuable than the tracer residence time, although it may have little theoretical

meaning. Initial tracer breakthrough provides water managers with an indication of the

length of time a contaminant will take to be detected at a downgradient receptor. However, the effects of longitudinal dispersion and inadequate sensitivity of current analytical

methods at extremely low concentrations render this situation meaningless.

31




3.3. Residence Time Skewness and Kurtosis

Tracer travel time skewness is a measure of the lateral asymmetry of the BTC and the

kurtosis is a measure of the peakness of the BTC. For impulse and short-pulse releases,

skewness may be determined from (modified from Mull et al., 1988, p. 58)

∞

0

(t − t

 ̄)

3 Q(t) C(t) dt

γt = ∞ (19)

0

σ3

t Q(t) C(t) dt

and the kurtosis may be determined from

∞

0

(t − t

 ̄)

4 Q(t) C(t) dt

κt = ∞ (20)

0

σ Q(t) C(t) dt 4

t

For continuous and long-pulse releases, the calculation of skewness is considerably more

difficult. In this instance skewness may be obtained from (Ravi Subramaniam, pers. comm.)

∞

0

∞

0

[3 − F(t)]t

2 dt − 6  ̄t [1 − F(t)]t dt + 2 t

 ̄3

γt = (σt

2)

3 (21)

and the kurtosis may be determined from

κt =

∞

0

[4 t − 12 t

 ̄− F(t)]t

2 dt + 12 t

 ̄2

∞

0

[1 − F(t)]t dt − 3 t

 ̄4 − 3 σt

22 (22)

A symmetrical curve results in a skewness coefficient equal to zero. Positive number

for the skewness indicates that the BTC is weighted to the right, recedes more gently than

it rises (Mull et al., 1988, p. 59), and reflects both longitudinal dispersion and dead zone

effects. Skewness is used by Qtracer2 only for comparison of dimensionless BTCs generated

from multiple tracer tests conducted from the same injection points to the same recovery

locations as described by Mull et al. (1988). Kurtosis is also used by Qtracer2 for comparison

purposes only for comparison of dimensionless BTCs generated from multiple tracer tests

conducted from the same injection points to the same recovery locations. Application of

skewness and kurtosis estimates is briefly discussed in Section 6.6.21. on page 86

3.3.1. Mean Tracer Velocity

Mean tracer velocity is a measure of the flow rate of the centroid of the tracer mass. For

impulse releases, mean tracer velocity is given by Equation (23) (modified from Gaspar,

32














1987b, p. 66)

∞ xs C(t) Q(t) dt

t

υ ̄ = 0

∞ (23)

C(t) Q(t) dt

0

with a standard deviation for impulse releases given by Equation (24)

∞ xs xs

	2

− C(t) Q(t) dt

 t t

 ̄ συ = 

0

∞ (24)

C(t) Q(t) dt

0

For short-pulse releases (t2 < t

 ̄), mean tracer velocity is given by Equation (25)

∞ xs C(t) Q(t) dt

0 t − t2/2

υ ̄ = ∞ (25)

C(t) Q(t) dt

0

with a standard deviation given by Equation (26)

∞ 
 
2



xs xs − C(t) Q(t) dt

0 t − t2/2 t

 ̄− t2/2

συ =  ∞ (26)

C(t) Q(t) dt

0

For long-pulse and continuous releases (t2 ≥ t

 ̄), mean tracer velocity is given by Equation (27)

xs υ ̄ = ∞ (27)

[1 − F(t)] dt

0

The standard deviation for long-pulse and continuous releases (t2 ≥ t

 ̄) cannot be solved

trivially and is not attempted here.

Tracer migration distance(s) is usually measured as a straight-line distance from the

injection point to the tracer recovery sampling station (radial distance = x [L]). A straightline assumption for solution conduits is unrealistic and should be corrected for sinuosity

(Field and Nash, 1997; Worthington, 1991, pp. 85–91) by

xs = Sd x (28)

33
where 1 ≤ Sd ≤ 3. Typically, Sd will be about 1.3 to 1.5 for most solution conduits. For

surface-water streams and tubes where the length can and has actually been measured or

reasonably approximated; (e.g., some traversable caves and mine tunnels) then Sd = 1.0

which should also be the accepted value for porous-media flow (unless a tortuosity value is

to be considered).

Estimation of the mean tracer velocity is an appropriate measure of the rate at which

the bulk of a nonreactive pollutant mass will migrate in a karst conduit. It also provides a

useful insight into the flow hydraulics of the conduit. Equations (23) and (27) also assume

that tracer residence time will vary from zero to instantaneous exit of the tracer mass from

the aquifer system.

Apparent tracer velocity is a measure of the rate of tracer migration as a function of

initial tracer breakthrough. It is obtained by dividing the distance traversed by the tracer

cloud by the time of first arrival of the tracer dye. Mean tracer velocity provides substantially

improved insight into aquifer functioning over apparent velocity.

Mull et al. (1988, p. 58) provide a simple equation for calculating mean tracer velocity.

Their equation is not reproduced here to avoid confusion. An example of its use is presented

later in this report (see Section 4. on page 48).

3.3.2. Longitudinal Dispersion

Longitudinal dispersion in surface and subsurface channels is similar to dispersion in closed

conduits and open channels. This is because conduit flow ranges from slow and laminar

to rapid and turbulent in subsurface channels that may exhibit either closed-conduit flow

or open-channel flow characteristics. Longitudinal dispersion works similarly for fracturedrock aquifers. The longitudinal dispersion coefficient is a measure of the rate at which a

concentrated tracer mass spreads out along the flow path (Mull et al., 1988, p. 59). It is

defined as the temporal rate of change in the variance of the tracer cloud (Fisher, 1968). It

is relevant to the analysis of karst conduits because it provides an indication of the amount

of possible spreading of a pollutant mass in terms of increasing persistence and decreasing

concentration over time.

Numerous studies on longitudinal dispersion have been conducted over the past few

decades (Chatwin, 1971; Sullivan, 1971; Day, 1975; Nordin and Troutman, 1980; Jobson,

1987; Reichert and Wanner, 1991), mostly with respect to open-channel flow. Longitudinal

and lateral dispersion for a slug release of tracer or pollutant in a flow channel will generally

appear as shown in Figure 12 and less so for a fracture-rock aquifer. In Figure 12, the

34
responses to a slug of injected tracer are shown with distance downstream from a single,

center slug injection along selected imaginary streamlines.

Figure 12. Lateral mixing and longitudinal dispersion patterns and changes in distribution

of concentration downstream from a single, center slug injection of tracer (Kilpatrick and

Wilson, 1989, p. 2).

As noted by Kilpatrick and Wilson (1989, p. 2), a soluble nonreactive tracer (e.g.,

some fluorescent dyes) released into a stream behaves in the same manner as the actual

water particles. Therefore, a measure of the movement of the tracer and its dispersion

characteristics will, in effect, be a measure of the movement of an element of fluid in the

stream. It may be further noted that the dispersion and mixing of the tracer in the receiving

stream takes place in all three dimensions (Figure 12), although vertical mixing normally

occurs before lateral mixing, depending on the flow characteristics and velocity variations.

Longitudinal dispersion, having no boundaries, continues indefinitely and is the dispersion

component of principal interest (Kilpatrick and Wilson, 1989, p. 2).

Longitudinal Dispersion by the Method of Moments Longitudinal dispersion is

most commonly estimated using the second moment (Ma�loszewskiand Zuber, 1992), which

when properly weighted for concentration, may be estimated for impulse, long-pulse (t2 ≥ t

 ̄),

35
 

  



and continuous releases by (Kreft and Zuber, 1978)

σ2 υ3

t DL = (29) 2xs

and for short-pulse releases (t2 < t

 ̄) by (Wolff et al., 1979)

DL = σt

2 − t2 υ3

. (30) 12 2xs

It should be recognized here that DL solved by (30) is based on the assumption of a

BTC and does not represent the mean residence time distribution as does (29). In some

instances, there will usually not be any major difference in DL estimation from (29) or (30).

Equations (29) and (30) assume that Fick’s law is always applicable; that is, there is

no anomalous behavior. In actuality, immobile-flow zones (dead zones) are common, which

cause a long tail to the BTC and invalidates Fick’s law.

Longitudinal Dispersion by the Chatwin Method Chatwin (1971) developed a

method for determining longitudinal dispersion intended to address the problem of nonFickian behavior. Technically, the Chatwin method is only really valid for impulse releases,

but it does provide a reasonable approximation for longitudinal dispersion for pulse and

continuous releases (see Section 8.1.1. on page 115). Longitudinal dispersion as developed

in Chatwin (1971) is given by Equation (31) as

Ap xs υ t  ̄ tln √ =  −  (31) C t 2 Dxs 2 Dxs 

where the proportionality constant, Ap represents (Davis et al., 2000)

M Ap =  (32) 2 A π Dxs 

For symmetrical concentration distributions (Davis et al., 2000),

xs =  ̄υt (33)

Ap C = Cp = √ (34) tp

which may be rearranged to yield

Ap = Cp tp (35)

36
  

 

 

Day (1975) showed that Equation (35) results in relatively insignificant errors for asymmetrical concentration distributions.

Subject to tκ ≤ xs/υ ̄, Equation (31) is reduced to the general least-squares problem by

solving

min	b − Ax	2

x 2 (36)

where

  1 t1

 1 t  

2

 A =  . .  (37)

 .

. .. 

1 tκ

x = (x1, x2)

T , (38)

b = (b1, b2, . . .,bκ)

T (39)

where T represents the transpose of the vector.

The parameters bi are equal to the left-hand side of Equation (31)

Ap bi = ti ln √ (40) C ti

and the parameters to be determined xi are equal to the two factors on the right-hand side

of Equation (31)

xs x1 =  (41) 2 Dxs 

υ ̄ x2 =  (42) 2 Dxs 

where x1 is the y intercept of the straight-line fit to the early-time data and x2 isthe slope

of the straight-line fit to the early-time data. Either term on the right-hand side allows

for solution of the longitudinal dispersion coefficient DL, provided that a plot of the lefthand side of Equation (31) against early-time data reasonably falls as a straight line (Day,

37
 

1975). The late-time data will depart from the straight line due to non-Fickian dispersion

characteristics (e.g., dead zones).

Equations (29) and (30) tend to overestimate DL, suggesting a greater BTC spread

than is likely to occur as a result of solute dispersion. Alternatively, Equation (31) may to

underestimate DL for systems exhibiting Fickian behavior.

In this report, Equation (31) is always used except in those instances where the Chatwin

method appears to fail or computer memory storage is exceeded. In that case, Equations (29)

and (30) are used as appropriate.

Mull et al. (1988, pp. 59–60) developed two equations designed to estimate the longitudinal dispersion coefficient of a karst conduit from dye-tracing studies. Results of the

two equations on the same data set produce radically different results. Their Equation (17)

appears to be the more reliable estimate for dispersion.

Smart (1988b) developed a relatively simple method of estimating the dispersion

coefficient based on the efforts of Brady and Johnson (1981), who used an equation derived

by Dobbins (1963). Although not described here, this method appears reasonable and

should be considered.

3.3.3. Tracer Dilution

Estimation of tracer dilution is desirable so that effective dilution of pollutant releases

may also be estimated. Given the generally nonconservative behavior of most tracers and

pollutants in hydrologic systems, as well as their basic differences, estimation of effective

dilution is recognized as a very rough approximation at best. Still, estimation efforts can

provide useful predictions about potential dilution in the system.

Longitudinal dispersion theory for a conservative tracer, released as a slug at t = 0

and x = 0 in densely fissured aquifers where dispersion and advection are assumed to be

one-dimensional, suggests that a uniform Gaussian distribution of the tracer concentration

will occur in the direction of flow as shown in Equation (9) of Dobbins (1963).

Min − (xs − υ t  ̄ )

2

C(xs, t) = √ exp (43) A 4πDL t 4DLt

Mass Min of the injected tracer is assumed to be small relative to the mass flux rate of the

water, so, in theory, the BTC should approach a Gaussian shape. In fact, the BTC is always

skewed to the right because of the effects of transverse dispersion (ignored in Equation [43]),

38


nonsteady flow conditions, and storage of tracer in very slow-moving water of small voids

with later release into large voids, which forms the “tail” of the BTC (Atkinson, 1987).

However, tracer behavior is considered to be sufficiently Gaussian-like to allow use of the

property of “complementarity.” Complementarity suggests that the effects of dispersion on

two tracer injections at successive times will proceed independently of each other, and that

the combined effect of the two injections will be the sum of their individual effects (Atkinson,

1987). This property was experimentally employed by Smart (1985) to demonstrate the

probable dilution estimation for a large quarry that had been used as a landfill for municipal

wastes.

Smart derived a dilution equation that utilized tracer input/output concentrations by

relating the mass of tracer injected into the aquifer from successive and repeated injections

to tracer recovery

Ci Mm D = = (44) CpL ∆tQCpL

Steady-state concentration CpL is a function of tracer recovery from a single tracer

injection and is given as

CpL =

j=tb+n ∆t

j=tb 

Cj (45)

where Cj is the tracer concentration at the resurgence at time j for a single instantaneous

tracer injection. Time tb represents the time between tracer injection and tracer breakthrough at the resurgence. The value n equals d/∆t, where d is the time between tracer

breakthrough and final tracer detection at the resurgence (pulse duration).

As may be observed from the above discussion, effective estimation of tracer dilution

in an aquifer is very difficult. Smart (1985) points out that as the tracer is not conserved

in the aquifer, dilution will be overestimated in proportion to the amount of tracer loss.

Effective estimation of tracer dilution is necessary, but much research is still needed.

3.4. FLOW-CHANNEL GEOMETRIES

Flow-channel geometries are estimated by evaluating discharge with respect to mean

residence time. This is accomplished for either the continuous or the discrete situation.

Not all the equations described in this section may be applied to analyses of porous-media

systems (e.g., granular aquifers), because of the need to know particle diameter, hydraulic

conductivity, and/or other factors.

39


3.4.1. Aquifer Volume

Tracer mass recovery, where discharge was measured during each tracer sampling event,

allows for a rough estimate of the maximum volume of flow system traversed by the tracer

cloud using of Equation (46) (Atkinson et al., 1973)

V =

t

 ̄

0

Q dt (46)

If a single discharge value is used as a mean discharge, then the volume may be estimated

by

V = Q t

 ̄ (47)

and a total maximum volume estimate based on the sum of each individual transport zone

(e.g., solution conduit or fracture) traversed by the tracer cloud may be determined from

Equation (48)

VT =

n

i=1

Vi (48)

It should be noted that aquifer volume calculations will be only a crude approximation

at best. Summing the volumes of individual transport zones to achieve a total maximum

volume estimate should not be expected to produce accurate results, but the sum of the

individual transport zones do provide some indication of the aquifer volume contacted

by tracer. However, Equations (46) and (47) provide a more realistic estimate of the

system volume than could be obtained from the product of mean discharge and time to

peak concentration, although this theory requires additional data for confirmation (Smart,

1988b).

By far, the majority of volume space will be occupied by micropores, but these contribute

little to the flow of ground water in solution conduits and fractures. As such, it is

recommended that investigators consider a variety of methods for estimating aquifer volume

and use all the data obtained for a better volume estimation.

Perhaps more valuable is a comparison between inflow rates and outflow rates. If

injection discharge is measured during tracer injection, comparisons may be made between

inflow and outflow that may lead to additional insights into the aquifer. For example,

inflow/outflow evaluations, coupled with comprehensive BTC analyses furnish a means, for

assessing the type of karst aquifer under investigation (Atkinson et al., 1973).

40


3.4.2. Cross-Sectional Area

The easiest and probably most reliable geometric parameter that can be estimated is crosssectional area. Because the volume V could be estimated from Equations (46) or (47), the

cross-sectional area may be estimated from

V A = (49) xs

where xs may be a sinuous distance or a straight-line distance. A sinuous distance will

result in a smaller A than a straight-line distance would suggest.

3.4.3. Flow-Channel Diameter

By assuming a cylindrical flow channel, it is possible to estimate a flow-channel diameter

from a BTC. Because the system volume has been estimated, the flow-channel diameter

may be obtained by

A DC = 2 (50)

π

Obviously, DC/2 can be used to estimate the flow-channel radius that is typically used in

many modeling endeavors.

3.4.4. Flow-Channel Hydraulic Depth

If open channel flow is assumed to occur in the flow channel, then a hydraulic depth may

be estimated by

A DH = (51) DC

which is a reasonable approximation.

3.4.5. Flow-Channel Surface Area

If the flow channel is assumed to conform to a cylinder, then it is possible to obtain an

initial estimate of the conduit surface area. (If it is also a solution conduit, then it needs to

conform to Karst Network Types I, II, VI, and VII.) A flow-channel surface area estimate

is obtained by

As = 2πrxsm (52)

41




The roughness correction factor m is necessary because the cylinder concept assumes a

“smooth as glass” cylinder. Roughness factor estimation is not straightforward and requires

some degree of professional judgment, especially if the flow channel of interest cannot be

directly entered to take physical measurements of roughness.

A reasonable estimate for the roughness factor may be obtained by

m = ε

δ/103 (53)

The surface irregularities relief ε, taken as 1.0 m, is considered reasonably representative

of typical flow-channel walls. There is some support for this assumption from natural river

beds (Chow, 1959, p. 196). The viscous-flow sublayer δ isdi vi ded by 103 in Equation (53)

to correct for obstructions in the flow regime created by scallops, differential dissolution,

large bends, undercut walls, breakdown, and backwater zones, as well as other possible

flow restrictions. These effects were considered by Atkinson (1977) to explain an estimated

roughness height equal to nearly three times the diameter of the solution conduit he was

investigating.

3.4.6. Tracer Sorption Estimation

Sorption to flow-channel walls can be estimated by considering a laboratory column as

analogous to flow through a channel. Although far from perfect, it can provide useful

information for comparison with more theoretically based models.

Karst conduit sorption is estimated by

Ka = (C0 − Cf )V (54) CfAs

and for multidischarge systems (e.g., Karst Network Types III and IV)

(C0 − Cf ) Vi Ka = (55) Cf Asi

If a multidischarge system is of interest, it is essential to note that any results obtained

by Equation (54) will be erroneous. Only results obtained by Equation (55) should be

considered relevant.

3.5. EMPIRICAL FLUID DYNAMICS MODELS

Experiments on fluid dynamics have led to the development of many models for flow for

specific geometries. These geometries will not necessarily be reproduced by the actual

42
 	

 	

hydrologic systems and cannot be reliably approximated, whether physical measurements

can be taken or not. However, by making some simple assumptions, reasonable parameter

estimates may be obtained. For solution conduits, it may be assumed that the phreatic

conduit will best be approximated by assuming a cylindrical conduit. Such an assumption

is not unreasonable for phreatic conduits developed in flat-lying sediments and may not be

too unreasonable for other structural and stratigraphic conditions.

3.5.1. P ́eclet Number

The P ́eclet number is a measure of the relative contribution of mechanical dispersion and

diffusion to solute transport. It relates the effectiveness of mass transport by advection

υxs ∂C = −P e ∂C −  ̄

Dxs ∂xs ∂xs to the effectiveness of mass transport by either dispersion or diffusion ∂2C (Schiesser and Silebi, 1997, p. 372). P ́eclet numbers below 0.4 indicate diffusion ∂x2 

s 

control; 0.4 − 6.0 suggests that diffusion and advection are in transition and thus approximately equal to each other; and > 6.0 indicates advection control (Fetter, 1992, pp. 54–55).

In most nonporous media instances of solute transport in karst conduits, P ́eclet numbers

will be greater than 6.0. Often, the P ́eclet numbers will be many times greater than 6.0.

Estimation of a P ́eclet number can be obtained from the calculated dispersion and mean

tracer velocity from

υ x ̄ s P e = (56) Dxs 

It is necessary to note that estimation of the P ́eclet number by Equation (56) may be too

low. Substitution of the peak flow velocity υp could be considered, but most likely would

result in overestimating the P ́eclet number.

It should also be noted here that even though xs is listed as representing distance, in

reality, for porous-media flow, it probably will not have been corrected for sinuosity.

3.5.2. Dynamic Flow Equations

Open-channel and closed-conduit flow phenomena are usually described by dimensionless

equations for flow behavior. The Reynolds number furnishes a means for determining if flow

is laminar or turbulent. The Froude number is used to determine if the flow is subcritical

or supercritical. The equations described in this section are not all applicable to analyses

of porous-media systems (e.g., granular aquifers) because of the need to know particle

diameter.

43


Reynolds Number The resistance of flow depends entirely upon the geometry and

ρ  ̄ magnitude of the quantityυ DC , where ρ represents fluid density, d conduit diameter, and ν ν

dynamic viscosity. The Reynolds number NR is the parameter describing the process. The

smaller the Reynolds number, the more resistance to flow. Assuming a cylindrical conduit,

a rough approximation of the Reynolds number for each individual sampling station may

be obtained from

NR = ρ υD ̄ C (57)

ν

Estimation of the Reynolds number by Equation (57) will be only a crude approximation

because the quantity (V/xs)1/2 is dependent upon a maximum volume estimate and a

straight-line radial distance to the sampling station. Consequently, V is immoderately

large, xs is immoderately small, and (V/xs)1/2 is excessively large. Therefore, calculation

of Reynolds number by Equation (14) should be regarded as an upper limit. However,

the quantity V/xs has been used to reasonably estimate the cross-sectional area of a single

uniform water-filled karst conduit in the Malign karst system (Smart, 1988b).

If the Reynolds number indicates flow to be in the laminar regime, then an equivalent

hydraulic conductivity K for flow within the conduit (or fracture) may be calculated. For

laminar flow in a karst conduit, K is obtained by

K = D2

Cρg (58) 8μ

and for laminar flow in a fracture, K is obtained by

K = new2ρg (59) 12μ

It should be noted that a hydraulic conductivity estimated by either Equation (58) or (59)

will be extremely large. In truth, K will be approaching infinity (imagine the value of K for

a lake). Hydraulic conductivity cannot be approximated for turbulent conditions because,

by definition, turbulent flow is a nonlinear phenomenon.

For porous-media flow, the Reynolds number uses the hydraulic conductivity in place of

the cylinder diameter (de Marsily, 1986, p. 74)

NR = υ ρ  ̄

μ

K μ (60) ρ g

although comparisons between Equation (57) and Equation (60) are inappropriate. Using

Equation (60) it may be accepted that laminar flow occurs when 1 ≤ NR ≤ 10, transient

flow occurs when 10 < NR ≤ 100, and turbulent flow occurs when NR > 100.

44
Froude number The ratio of the mean flow velocity to the linear dimension of flow

(hydraulic mean depth) is a measure of the extent to which gravitational acceleration affects

flow. Gravity becomes less important as the ratio increases. Such a ratio is useful for

determining if flow is in the subcritical or supercritical range. The parameter describing the

effect is the Froude number and is given by

υ ̄ NF = √ (61) gDH

Estimation of the Froude number by Equation (61) will be a rough approximation mainly

for the same reasons that apply to the Reynolds number estimation. The Froude number is

used to explain flow behavior for streams with a free surface, which may increase uncertainty

because subsurface channels may exhibit either open-channel flow, closed-conduit flow, or

both flow types depending on stage.

An estimated Froude number for a flow channel exhibiting closed-conduit flow (e.g.,

karst conduits) is not appropriate. Also, as presented, the calculation for the Froude number

assumes that the cross-sectional area of the flow channel, divided by the diameter of the

flow channel, is equal to the mean hydraulic depth, which may not always be true.

3.6. BOUNDARY-LAYER EFFECTS

While not generally considered in tracing studies, boundary-layer effects can substantially

impact the study results. In most instances, flow-channel walls are assumed to be smooth,

which is unreasonable. Cave exploration and fractured-rock studies have revealed that

conduit walls are often covered with scallops, making them very rough. Additionally,

sediment coating on cave walls and layering on cave floors greatly adds to roughness and

surface area. Cave breakdown is an extreme case causing significant roughness. The

equations described in this section are not applied to analyses of porous-media systems

(e.g., granular aquifers) because of the need to know particle diameter.

3.6.1. Friction Factor Estimation

When flow is believed to be laminar, a friction factor may be estimated by (White, 1988,

p. 163)

64 ff = (62) NR

and for turbulent flow, a friction factor may be estimated by (White, 1988, p. 163)



1 DC = 2 log + 1.14 (63) ff ε

45
where the relief of surface irregularities ε is a controlling factor and depends on the nature

of the channel through which flow is occurring.

3.6.2. Viscous-Flow Sublayer

It is well documented by empirical studies that turbulent flow occurs as a core that

is surrounded by a viscous-flow sublayer. The thickness of the viscous-flow sublayer is

dependent on the degree of channel-wall roughness. If a typically very rough flow channel

is assumed, then the viscous-flow sublayer may be estimated by (White, 1988, p. 163)

δ 32.8 =  (64) DC NR ff

which is an important parameter for assessing the extent of solute sorption to channel walls

and the possibility of matrix diffusion effects. Matrix diffusion can occur only from the

viscous-flow sublayer.

3.6.3. Hydraulic Head Loss

When flow is laminar, the hydraulic head loss along a channel can be estimated by (modified

from White, 1988, p. 162)

8.0μυx ̄ s hL = ρgr2 (65)

and when flow is turbulent, the hydraulic head loss along the channel may be estimated by

(White, 1988, p. 163)

ffxsυ ̄2

hL = (66) 4gr

which emphasizes the influence of friction on head loss.

Hydraulic head loss in porous media is based on a rearrangement of Darcy’s law (modified

from White, 1988, p. 162)

υ x ̄ s hL = (67) K

It should be noted here that even though xs is listed here as representing distance, in reality

it probably will not have been corrected for sinuosity.

46


3.6.4. Shear Velocity

The shear velocity for flow through a flow channel is created by boundary-layer effects

produced by the channel walls. Therefore, it might be expected that the shear velocity will

be somewhat less than the flow velocity in the center of the channel.

Estimation of the shear velocity is obtained by

A hL

υs = g (68) DC xs

It will be noted that flow velocities produced by Equation (68) will always be less than

those produced by Equation (23). This makes sense in that the flow channel walls should

impart some negative influence (i.e., resistance) on the flow velocity.

47
4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY

To determine the total mass recovery of tracer injected into a hydrologic system, the following steps must be initiated. The example calculations describe a scenario in which time is

measured in hours and discharge calculations are in SI units, to facilitate the explanation.

Simple modifications to the procedure may be made for units that vary from the example.

1. Plot the Concentration Subtract background tracer concentration. Plot the concentration of tracer recovered (e.g., mg L−1) versus time in appropriate units (e.g., h).

Ti me should be plotted on the x axi s.

2. Plot the Discharge If the tracer is being recovered at a sampling location (e.g., spring

or well) where discharge is variable over the time of tracer recovery, then plot discharge

in appropriate units (e.g., m3 s−1) versus time (hours) also. Again, time should be

plotted on the x axis. If discharge is constant there is no need to plot discharge.

3. Integrate Recovery Curve Quantitation of tracer recovery is found by integrating

everywhere underneath the tracer recovery curve according to Equation (11), which

must be integrated numerically. This is done using a simple summation algorithm.

This is most easily accomplished by setting up a table that facilitates the necessary

calculations (Table 4).

Table 4. Table representing tracer recovery data for processing.

Sample t Q C C × Q t × C × Q

(T) (L3 T−1) (M L−3) (M T−1) (M)

··· ··· ··· ··· ··· ··· . . . . . . . . . . . . . . . . . .

··· ··· ··· ··· ··· ···

4. Integrate Recovery Curve Again Integrating the recovery curve a second time, but

this time including time t, and dividing by the mass recovered (step 3 above) according

to Equation (14), will yield the mean residence time. This is most easily accomplished

by using the table created in step 3 above (Table 4), which facilitates the necessary

calculations. Time is recorded in equally spaced increments. If discharge was constant

during the period of tracer recovery, then the Q column (column 3) of the table has a

48
 

constant value as well. The C × Q column (column 5) is obtained from the product

of the third and fourth column values. The t × C × Q column (column 6) is obtained

from the product of the C ×Q column with the t column (column 1), and by applying

all necessary conversions (e.g., hours vs. seconds).

5. Calculate Tracer Mass Recovery When the table of values is complete, Equation (11) can be solved by summing column 5 and multiplying by a time conversion to

get units of mass only. Hence, the solution to Equation (11) is acquired in a simplified

manner by

MO =

∞

0

Q(t)C(t)dt ≈

n

i=1

QiCi∆ti ≈ tc

n

i=1

(QiCi) (69)

where tc is any necessary time conversion factor that allows for units of mass.

6. Calculate Mean Tracer Residence Time Mean tracer residence time t

 ̄ is found by

solving Equations (14) and (17). Equations (14) and (17) are solved by the same

method that Equation (11) is solved; by simplified summation of the data. Using

Table 4, summing column 6, and multiplying by the appropriate conversion factor to

get units of concentration–time. Divide the mass obtained in step 5 above into this

number to obtain units of time.

7. Calculate Mean Tracer Velocity Divide the distance traversed by the tracer cloud

by the mean tracer residence time to obtain mean tracer velocity.

8. Calculate Longitudinal Dispersion If the method of moments is used to solve for

longitudinal dispersion the basics of steps 3 and 4 above are repeated to create Table 5.

Columns 4 and 5 are again summed and the results converted to appropriate units.

Then Equations (29) and (30) are applied depending on the type of tracer release.

Alternatively, if the Chatwin method is used, Table 6 is set up using legitimate values

Table 5. Table representing tracer recovery data for processing.

Sample (t − t

 ̄) 2 Q C C × Q (t − t ̄) 2 × C × Q

(T2) (L3 T−1) (M L−3) (M T−1) (M T)

··· ··· ··· ··· ··· ··· . . . . . . . . . . . . . . . . . .

··· ··· ··· ··· ··· ···

49
for time (0 < tκ ≤ xs/υ ̄), and solved parameters for bi (Equation [40]) representing

the Chatwin designation. A straight line is then drawn through the legitimate values,

and longitudinal dispersion is solved using either Equation (41) or (42).

Table 6. Table representing Chatwin values.

Sample Time Chatwin Fit Residual

(h) (s1/2) (s1/2) (dimen.)

··· ··· ··· ··· ··· . . . . . . . . . . . . . . .

··· ··· ··· ··· ···

9. Repeat for Subsequent Sampling Stations Repeat the above steps for all wells

and/or springs in which the tracer was recovered.

10. Calculate Total Tracer Mass Recovery If several wells and/or springs recovered

the tracer, then sum the individual masses obtained for each well and each spring

together to obtain the total tracer mass recovered.

11. Calculate Percent Mass Recovered Calculate the percentage of mass recovered by

dividing the quantity of tracer mass recovered by the quantity of tracer mass injected

and multiplying the result by 100.

12. Calculate Additional Parameters Calculate the P ́eclet number, Reynolds number,

etc. as desired and appropriate, using the equations developed in Section 3. on page 26

4.1. SIMPLIFIED EXAMPLE CALCULATION

Four hundred and thirty-five kilograms of sodium chloride, NaCl (264 kg Cl−) (RCA, 1992),

were injected into the north coast karst aquifer over a period of 24 minutes (0.4 hour) at the

RCA del Caribe (Barceloneta, Puerto Rico) Superfund site for a tracing study. Injection

occurred at a rate of 13.75 gpm (8.78×10−4 m3 s−1) at 940 feet (287 m) below land surface

(BLS), which is also below the confining layer for the bottom of the shallow aquifer.

The leakage rate from the deep aquifer up the annular space to the shallow aquifer was

450 gpm. The total height that the tracer needed to rise to reach the shallow aquifer was

240 feet (73 m) or 700 feet (213 m), BLS. The time down the well (940 feet) was 11.18

minutes, and the rise up the annular space 240 feet was 1.08 minutes for a total reduction

50
   

   

of the time of travel by 12.26 minutes (0.2 hour), and a consequent increase in the flow

velocity according to Equation (2).

Recovery was at an observation well 110 feet (34 meters) from the injection well that

was pumped at a constant rate of 6.0 gpm (3.79 × 10−4 m3 s−1). Figure 13 displays the

BTC for the RCA del Caribe Superfund site, and Table 7 (slightly modified from Table 4)

displays the tracer recovery data and estimation methods for the zeroth and first moments.

4.1.1. Mass Recovery Example

Tracer mass recovery is found by solving Equation (11) or, more simply, by Equation (69).

Equation (69) is solved for tracer mass recovery by multiplying the measured concentration

values by the measured discharge values after correcting for consistent units and then

summing the results. Column 6 of Table 7 lists the products of columns 4 and 5 and

is summed at the end.

The summed results of column 6 of Table 7 must be multiplied by 3,600 seconds because

time is recorded in hours, but the analyses used seconds.

−1 4.85 × 102 mg s 3.60 × 103 s = 1.75 × 106 mg

= 1.75 kg

As shown, 1.75 kg of Cl

− were recovered. Because 264 kg of Cl− was injected into the

aquifer, it is evident that only 0.66% of the original tracer mass was recovered. Clearly a

serious mass balance problem exists. It may be noted that Equation (69) is not as precise

as Equation (11). However, results obtained by Equation (69) will generally be found to be

more than adequate in most instances.

4.1.2. Mean Residence Time Example

Tracer residence time is found by solving Equation (14) or its equivalent discrete form. This

is accomplished by multiplying column 6 by column 3 in Table 7, and recording the results

in column 7. Summing column 7 of Table 7, and multiplying by 3,600 seconds will yield

results in units of mass–time

1.54 × 107 mg 3.60 × 103 s = 5.54 × 1010mg s

51
Figure 13. Tracer-breakthrough curve for the RCA de Caribe Superfund site.

52
Table 7. Discharge values and tracer recovery values at specific times.

Sample t Q C C × Q t × C × Q

(h) (m3 s−1) (mg m−3) (mg s−1) (mg)

1 0.00

2 1.00

3 2.00

4 3.00

5 4.00

6 5.00

7 6.00

8 7.00

9 8.00

10 9.00

11 10.00

12 11.00

13 12.00

14 13.00

15 14.00

16 15.00

17 16.00

18 17.00

19 18.00

20 19.00

21 20.00

22 21.00

23 22.00

24 23.00

25 24.00

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

0.00 × 100

0.00 × 100

0.00 × 100

0.00 × 100

0.00 × 100

5.00 × 103

2.50 × 105

3.80 × 105

2.00 × 105

1.25 × 105

7.50 × 104

5.50 × 104

4.00 × 104

2.50 × 104

2.00 × 104

1.50 × 104

1.40 × 104

1.30 × 104

1.20 × 104

1.10 × 104

1.00 × 104

9.00 × 103

8.00 × 103

7.00 × 103

6.00 × 103

n

i=1

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

1.89 × 100 3.41 × 104

9.46 × 101 2.04 × 106

1.44 × 102 3.63 × 106

7.57 × 101 2.18 × 106

4.73 × 101 1.53 × 106

2.84 × 101 1.02 × 106

2.08 × 101 8.25 × 105

1.51 × 101 6.54 × 105

9.46 × 100 4.43 × 105

7.57 × 100 3.82 × 105

5.68 × 100 3.07 × 105

5.30 × 100 3.05 × 105

4.92 × 100 3.01 × 105

4.54 × 100 2.94 × 105

4.16 × 100 2.85 × 105

3.79 × 100 2.73 × 105

3.41 × 100 2.58 × 105

3.03 × 100 2.40 × 105

2.65 × 100 2.19 × 105

2.27 × 100 1.96 × 105

4.85 × 102 1.54 × 107

Note: “Sample” arbitrarily assumes that the first sample was collected at the

time of injection.

Time t is listed here in hours, but is converted to seconds before

multiplying with C and Q.

(source: RCA, 1992)

53
 

Dividing by the mass recovered (1.75 kg) will yield the mean residence time of the tracer in

units of time.

5.54 × 1010 mg s = 3.17 × 104 s

1.75 × 106 mg

= 8.79 × 100 h

This is necessarily corrected for time to reach the flow zone (tinf = 0.2 h)

8.79 × 100 h − 2.0 × 10−1 h = 8.59 × 100 h

Apparently, it took less than 9 hours for the Cl

− tracer to reach the recovery well.

4.1.3. Mean Tracer Velocity Example

Mean tracer velocity is obtained from Equation (25) or, more simply, by dividing the distance

to the sampling station by the time of travel, minus one half the pulse-injection time, which

is a modification of Equation (2)

34 m = 4.05 × 100 m h−1

(8.79 h − 0.2 h) − 0

2

.4 h

−1 = 1.13 × 10−3 m s

This may then be used to estimate the velocity of a nonreactive pollutant, assuming that

this value is representative of the prevailing ground-water flow velocity. If the tracer used

is of known reactivity with the aquifer, then it may be related to a pollutant of similar

reactivity to estimate retardation.

The difference between the perceived velocity and the actual velocity may then be

obtained from Equation (3)

34 m (0.2 h) = 9.22 × 10−2 m h−1

(8.79 h − 0.2 h) 8.79 h

which suggests a relatively insignificant difference of 0.1mh−1 for this example.

4.1.4. Longitudinal Dispersion Example

Longitudinal dispersion is most accurately estimated by the Chatwin method (Equation [31]), which can be tedious. Using just the first valid time value, Equation (40) appears

as

√  3.80 × 105 2.52 × 104

bi = 1.80 × 104 ln √ = 284.57 s

1/2

5.0 × 103 1.80 × 104

54
  
 


Table 8. Chatwin parameter values for the RCA data set.

Sample Time Chatwin Fit Residual

(h) (s1/2) (s1/2) (dimen.)

6 5.0 284.57 266.33 18.24

7 6.0 103.48 132.01 -28.52

8 7.0 0.00 -2.32 2.32

9 8.0 -128.70 -136.65 7.96

10 9.0 -178.75 -270.98 92.23

11 10.0 -228.03 -405.31 177.28

12 11.0 -259.98 -539.64 279.66

13 12.0 -292.60 -673.97 381.37

14 13.0 -335.96 -808.30 472.33 . . . . . . . . . . . . . . .

25 24.0 -552.44 -2285.91 1733.47

after converting the time and concentration values to consistent values (seconds and mg m−3

[μ L−1], respectively for this example). Partial results for the RCA example data set are

shown in Table 8. Samples collected prior to t = 5.0 hours were devoid of tracer (C = 0.0

mg L−1), so the first legitimate sample for consideration for the Chatwin analysis occurs at

5.0 hours. According to the limit tκ ≤ 8.40 h (see Section 3.3.2. on page 34), only samples

6–9 listed in Table 8 are considered valid for the Chatwin analysis (assuming that sample

1 [Table 4] represents time zero). A casual inspection of Table 8 will indicate that residual

errors (Chatwin value minus the Fit value) after sample 9 become increasingly large further

indicating the inappropriateness of samples 10–25.

Also, it should be noted that while time values listed in Table 8 are in hours, the Chatwin

and Fit values are listed in seconds to the one-half power. The Fit values are obtained by

fitting a straight line through the Chatwin values plotted against time. The choice of units

does not matter provided, appropriate corrections are made to the final dispersion estimates.

Using samples 6–9, longitudinal dispersion by the Chatwin method is DL = 1.15 m2 h−1

and a corresponding P ́eclet number is obtained from Equation (56)

34 (4.05) Pe = = 120.74 1.15

If the method of moments are used to solve for longitudinal dispersion (Equation [30]), then

DL = 12.75 − 0.4 (4.05)3

= 12.42 m2 h−1

12 2 (34)

55
   

   

where σt

2 = 12.75 hours was obtained from Equation (17) in summation form (Table 9)

similar to the method used to obtain the mean resident time (Table 7).

As with Table 7, column 5 in Table 9 is multiplied by column 2 in Table 9 and the results

recorded in column 6. Summing column 6 of Table 9 and multiplying by 3,600 seconds will

yield results in units of mass–time

2 2.23 × 107 mgs 3.60 × 103 s = 8.03 × 1010mg s

Dividing by the mass recovered (1.75 kg) will yield the time of travel variance of the tracer

in units of time.

8.03 × 1010 mg s2

2 = 4.59 × 104 s

1.75 × 106 mg

= 12.75 × 100 h2

The P ́eclet number is now obtained as Pe = 11.09.

4.1.5. System Volume

The flow system volume may be estimated using Equation (47). The average discharge for

the RCA del Caribe site, 3.79 × 10−4 m3 s−1 (6 gpm), is multiplied by the mean residence

time, 3.09 × 104 s, to obtain the system volume.

−1 3 3.79 × 10−4 m s 3.09 × 104 s = 1.17 × 101 m

Apparently, only a small volume of the aquifer was utilized by the tracer to arrive at the

recovery well, which was expected, given the poor mass recovery.

56


Table 9. Table of values used to determine the time of travel variance.

Sample (t − t

 ̄) 2 Q C C × Q (t − t ̄) 2 × C × Q

(h2) (m3 s−1) (mg m−3) (mg s−1) (mg s)

1 7.40 × 101

2 5.78 × 101

3 4.36 × 101

4 3.14 × 101

5 2.12 × 101

6 1.30 × 101

7 6.79 × 100

8 2.58 × 100

9 3.66 × 10−1

10 1.56 × 10−1

11 1.95 × 100

12 5.74 × 100

13 1.15 × 101

14 1.93 × 101

15 2.91 × 101

16 4.09 × 101

17 5.47 × 101

18 7.05 × 101

19 8.83 × 101

20 1.08 × 102

21 1.30 × 102

22 1.54 × 102

23 1.79 × 102

24 2.07 × 102

25 2.37 × 102

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

3.79 × 10−4

0.00 × 100

0.00 × 100

0.00 × 100

0.00 × 100

0.00 × 100

5.00 × 103

2.50 × 105

3.80 × 105

2.00 × 105

1.25 × 105

7.50 × 104

5.50 × 104

4.00 × 104

2.50 × 104

2.00 × 104

1.50 × 104

1.40 × 104

1.30 × 104

1.20 × 104

1.10 × 104

1.00 × 104

9.00 × 103

8.00 × 103

7.00 × 103

6.00 × 103

n

i=1

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

0.00 × 100 0.00 × 100

1.89 × 100 8.85 × 104

9.46 × 101 2.31 × 106

1.44 × 102 1.33 × 106

7.57 × 101 9.97 × 104

4.73 × 101 2.66 × 104

2.84 × 101 1.99 × 105

2.08 × 101 4.30 × 105

1.51 × 101 6.28 × 105

9.46 × 100 6.58 × 105

7.57 × 100 7.93 × 105

5.68 × 100 8.36 × 105

5.30 × 100 1.04 × 106

4.92 × 100 1.25 × 106

4.54 × 100 1.44 × 106

4.16 × 100 1.62 × 106

3.79 × 100 1.77 × 106

3.41 × 100 1.88 × 106

3.03 × 100 1.96 × 106

2.65 × 100 1.98 × 106

2.27 × 100 1.94 × 106

4.85 × 102 2.23 × 107

Note: “Sample” arbitrarily assumes that the first sample was collected at the

time of injection.

Time (t − t

 ̄) 2 is listed here in hours2, but is converted to seconds2 before

multiplying with C and Q.

57
5. QTRACER2 COMPUTER PROGRAM DESCRIPTION

To facilitate calculation of total tracer recovery and related information, a FORTRAN

computer program has been developed (Field and Nash, 1997). A CD containing the

executable file and data files is contained at the end of this document. The program uses a

reliable and efficient integration algorithm that takes advantage of an efficient interpolation

algorithm (Kahaner et al., 1989, pp. 81–137) and/or extrapolation routines if desired.

5.1. DATA INTERPOLATION

The interpolation algorithm used in the FORTRAN program develops a “piecewise cubic

Hermite” function. The interpolant is defined in terms of a set of cubic polynomials, each

of which is defined between pairs of consecutive data points. The coefficients of these cubic

polynomials are chosen so that the interpolant has continuous first derivatives, which makes

it a “Hermite” interpolant. This is not enough to uniquely determine the interpolant, and

the remaining freedom of choice is used to ensure that the interpolant is “visually pleasing,”

meaning that monotonicity in the data results in monotonicity in the interpolant (i.e., the

interpolant does not have extraneous “wiggles”). A piecewise cubic Hermite function, in

effect, produces the most reasonable interpolation of the data possible.

5.2. DATA EXTRAPOLATION

Data extrapolation may be used if tracer sampling has ceased prior to complete tracer

recovery. Extrapolation may be used to predict the time at which zero (or near zero) tracer

concentration would have occurred had tracer sampling been continued until complete tracer

recovery was accomplished. The program extrapolates the data by three separate methods.

5.2.1. Exponential Decay

The first and most hydrologically based method uses an exponential decay function in which

five additional points are created to produce a reasonably smooth decay curve. This method

is based on the concept that most BTCs, in which complete recovery was obtained, exhibit

exponential decay. Using this method prevents the newly extrapolated data from ever

reaching zero (or background) concentration. In reality, it would go to infinity if allowed.

To overcome this problem, the program approximates the best stopping location.

58
5.2.2. Piecewise Cubic Hermite

The second method relies on the cubic Hermite function to find the single most reasonable

stopping data point for extrapolation. This is achieved by using the entire BTC to

develop a smooth function, based on the shape of the overall curve, and then producing

an appropriately chosen extrapolation point. Unfortunately, because the curve has rising

and descending limbs and at least one peak (multiple peaks are not uncommon), excessive

extrapolation will cause extrapolation to rise incorrectly. A stopping criteria is used to

prevent extrapolation from proceeding in a rising fashion. The net effect is to cause

extrapolation to cease prior to zero concentration being reached in most instances. In

some instances, even an acceptable decrease may not be achieved.

5.2.3. Straight-Line Projection

The third method for data extrapolation is achieved by projecting data for the decreasing

limb of the BTC beyond the last measured time-concentration data point, such that zero

tracer concentration is achieved. This is accomplished by projecting a line from the last

peak value through each of the measured (or interpolated) data points on the decreasing

limb to the x axis and storing the new data point in an array. The greatest cluster of the

new data array is then used to estimate a final time value for zero tracer concentration.

5.2.4. Extrapolating Discharge

Extrapolation of discharge data is a virtual unknown. It is determined here by taking the

midpoint of the measured late-time discharge data limb as the endpoint and extending the

discharge curve to equal the extrapolated late-time data. If the measured discharge data

are decreasing, then the extrapolated discharge data will increase to one-half the original

decreasing value. If the measured discharge data are increasing, then the extrapolated

discharge data will decrease to one-half the original increasing value.

Extrapolating the data beyond measured values is very risky and may lead to serious

errors in the analyses. However, used cautiously, extrapolation of the data may lead to

additional insights into aquifer hydraulics.

5.3. CHATWIN’S ESTIMATION OF LONGITUDINAL DISPERSION

Calculation of longitudinal dispersion is accomplished by fitting a straight line through a

plot of the Chatwin Parameter versus statistically determined early-time data using an

59
efficient singular value decomposition routine (Kahaner et al., 1989, pp. 218–223), a routine

chosen because degenerate data may prevent a straight-line calculation by either a leastsquares method or by the normal equations. Singular value decomposition always produces

a straight-line fit to the data (Vetterling et al., 1992, p. 197). Evaluation of the fit is provided

by statistical calculation of the coefficient of determination (R2), the correlation coefficient

(r), the probability of the fit, and Fisher’s z statistic. R2 should approach a value of 1 for

a good fit, r should approach a value of -1 for a good fit (for the Chatwin Parameter), the

probability of the fit should be a very small value, and Fisher’s z statistic may be used in

additional statistical tests if desired (Press et al., 1992, pp. 632–633).

Because of memory limitations typical of PCs, there can be instances in which large data

files exceed the ability of the data arrays to provide sufficient storage for Chatwin’s method

of analysis. When this occurs, the method of moments is automatically applied according

to Equations (29) and (30). Using Equations (29) or (30) will almost always result in an

overestimation of dispersion, which should be realized.

5.4. DATA NORMALIZATION

Individual tracer tests conducted at the same injection/recovery stations under differing

hydrologic conditions should be compared to obtain information regarding aquifer behavior

under varying conditions. Normalized tracer concentration files, normalized tracer load

files, and standardized tracer concentration files can be calculated by QTRACER2 and may

be analyzed according to the method described by Mull et al. (1988). The discussion by

Mull et al. is very comprehensive and, therefore, is not repeated here. Another reason for

not repeating the Mull et al. discussion here, is because of the probability that in most

instances, the tracing site (1) may have multiple discharge locations, many of which may

not be continuously monitored for tracer; and (2) may require more quantitative tracing

experiments than can be reasonably undertaken.

5.5. RANGE OF POSSIBILITIES OF QTRACER2

QTRACER2 can be used on almost any type of tracer test in any kind of geological

environment (e.g., surface water, porous media, fractured-rock aquifer, or karst aquifer).

This may sound strange, but the statement is true because the basic equations for mass

balance are not dependent on geological conditions.

QTRACER2 was initially designed to be used in karst systems primarily, but it will

handle any other typical hydrological system (e.g., fractured-rock systems) reasonably

60
well when told to do so in the sampling station data file. It may be used to evaluate

BTCs from tracer tests conducted in surface water and porous media by entering the

relevant information in the sampling station data file(s) and dummy information where

the information is irrelevant. The user will then need to note when the output data make

sense. By exercising some basic judgment, QTRACER2 can be effectively used in a variety

of environments.

5.6. COMPUTER GRAPHICS

A high-quality color graphics algorithm, PGPLOT1 (Pearson, 1997), that allows cascading

of graphics screens, direct printing, creation of screen files, etc., using pull-down menus

in the Windows environment has been included in QTRACER2. (The original interactive

capabilities developed by Kahaner and Anderson (1990), and utilized in QTRACER are

no longer available.) The graphics routine used here also provides for visual examination

of the data files and other relevant information (e.g., statistics when appropriate). It is

particularly useful for evaluating the effect of interpolating and/or extrapolating the original

data. Publication quality plots may be generated as postscript files from the graphics screen

incorporated into the program. Alternatively, a screen dump using any type of printer is

possible.

5.6.1. Features of the Interactive Graphics Loop

Running QTRACER2 starts a conventional Windows screen with a series of pull-down

menus (Table 10). Each underlined character in Table 10 indicates that the Alt key plus

the underlined character implements the respective menu item. For example, Alt+F initiates

the pull-down menu items underneath the File heading. Of course, the mouse pointer can

be used to access the menu items.

It i s necessary to poi nt out here that most users wi ll not use the pull-down menus

often. Most of the more useful graphics functions have been built directly into QTRACER2

to alleviate excess work by the user. However, in some instances, the user may find the

functions of value. For example, selecting the Cascade function under the Window pull-down

menu after a total five or six graphics plots have been produced in a series of child-windows,

will cause the child-windows to stack, slightly offset to the lower right.

1PGPLOT may be obtained from http://www.astro.caltech.edu/∼tjp/pgplot/

61
Table 10. Pull-down menu items available in QTRACER2.

File Edit View State Window 

62

Print... Select Text

Save...Exit Ctrl+C Select All

Select Graphics

Copy Ctrl+Ins

Paste

Size To Fit Pause Ctrl+S Cascade 

Full Screen Alt Enter Tile

Arrange Icons

Iput

Clear Paste

Status Bar

1Graphic 1

2PGPlot Graphics, # 1

...
File Items listed under this heading are described as follows.

Print... A screen dump to the local printer attached to the respective PC. 

S

Exit Ctrl+C Exit the program. 

ave... Save the screen as a bitmapped (*.BMP) file. 

Edit Items listed under this heading are described as follows.

Select Text Select text for pasting to the clipboard. 

Select graphics for pasting to the clipboard. 

Select

Copy C trl+Ins Copy selected items to the clipboard. 

All Select both text and graphics for pasting to the clipboard. 

Select Graphics 

Paste Paste selected items to the screen. 

View Items listed under this heading are described as follows.

Size To Fit Fit the graphics screen to the view surface without scroll bars. 

Full Screen Alt+En ter Fit the entire graphics screen to the view surface without the menu 

items displayed (a left-mouse click returns to the original screen). 

State Items listed under this heading are described as follows.

Pause Ctrl+S Pause the graphic display. 

Resume Ctrl+Q Resume graphic display. 

The two items Pause and Resume appear only as alternates of each other so that only the

one that is not currently functioning is accessible. The item that is currently in operation

is not displayed in the pull-down menu.

63
Window Items listed under this heading are described as follows.

Cascade Allows for a cascading view of multiple child windows at one time. 

Tile Allows for a tile display of multiple child windows at one time. 

Arrange Icons Not currently used in QTRACER2.

Input Automatically displays the input screen (Graphic 1) for data input. 

Clear Paste Clears an item pasted onto the screen. 

Status Bar Displays the current operating mode of the displayed graphics screen in a bar at the 

bottom of the screen (when “check marked”). 

1 Graphic 1 Name of the data input screen (“check marked”) if active. 

2 PGPlot Graphics, # 1 Identifying name/number of all subsequently opened graphics screens 

(active when “check marked”). 

Help Items listed under this heading are described as follows.

C

Using Help Describes the use of 

ontents Listing of available help contents. 

the Help function. 

About Identifies the current version of QTRACER (Version 2.0).

5.7. QTRACER2 SOURCE

The FORTRAN source for QTRACER2 is included on the CD. It is a very large program

that had to be split into pieces to allow its use on a PC. It is not recommended that users

attempt to follow the logic or modify the program. Questions regarding the program’s

functioning can be addressed to the author.

In addition, the graphics routine developed at the California Institute of Technology is

included. This program is not allowed for use for commercial products.

64
6. USING QTRACER2

The QTRACER2 program for BTC analysis is an easy-to-use computer package that

requires little more from the user than pressing <ENTER> when requested or manipulating

pull-down menus with a mouse. However, QTRACER2 does require creating data-input

files first for processing. Using data-input files rather than requiring interactive responses

to questions posed by the program facilitates more rapid data processing while minimizing

the opportunities for incorrect data entry.

6.1. QTRACER2 PROGRAM AND EXAMPLE DATA FILES

Before running the program, the user should copy all QTRACER2 files to the hard drive

and put the supplied CD-ROM disk in a safe place. Although the CD-ROM has plenty

of storage space for the creation of data-output files and graphics files, the possibility of

damage to the QTRACER2 program file from excess use cannot be ignored.

6.1.1. Loading QTRACER2 and Example Data Files

1. After “booting” up the computer, place the CD-ROM into the CD-ROM drive.

2. At the computer “desk top” place the mouse pointer (arrow) on the “My Computer”

icon and click the Right mouse button (Right Click).

3. Left Click on the word “Explore” in the pop-up menu. Alternatively, just press the

letter “E” on the keyboard.

4. Place the mouse pointer on the CD-ROM drive icon (e.g., D: or E:) and Left DoubleClick.

5. Left Click “Edit” at the top of the Window Screen and Left Click on “Select All” in

the pull-down menu. Alternatively, just press the letter “A” on the keyboard.

6. Left Click on the “Copy” icon on the “Tool Bar” near the top of the Window Screen

(second row). Alternatively, Left Click on “Edit” at the top of the Window Screen

and then Left Click on “Copy” or just press “C” on the keyboard.

7. Left Click on the preferred hard drive (e.g., C:).

65
8. Left Click on the “Paste” icon on the “Tool Bar” near the top of the Window Screen

(second row). Alternatively, Left Click on “Edit” at the top of the Window Screen

and then Left Click on “Paste” or just press “P” on the key board.

A Folder named Qtracer2 will be created on the chosen hard drive and all the appropriate

files copied accordingly to the appropriate file folders2.

6.2. QTRACER2 EXECUTION

QTRACER2 is very easy to use. Once the appropriate data files are created (which are

nearly self-explanatory) QTRACER2, for the most part, requires nothing more than pressing

the <ENTER> (<RETURN>) key as requested or manipulation of the mouse and clicking with

the left-mouse button.

1. In Windows Explorer, Left Double-Click the QTRACER2 folder and then Left DoubleClick the QTR.EXE file which will initiate program operation.3

2. The program prompts the user to enter the file to be evaluated (unless a file was

specified when starting the program using a DOS prompt). Press <ENTER> to

automatically run the default file, QTRACER.D, which calls QTRACER.DAT (these two files

correspond with ATKIN.D and ATKIN.DAT from the original QTRACER Version 1.0,

respectively). However, if the data files are in different locations from QTRACER2,

the user must provide the correct path to the *.D and *.DAT files. One advantage

of creating a subdirectory on the hard disk is that the program will find all files

automatically because they are all at the same location as the executable file.

2The first version of Qtracer was designed for MSDOS�R use and required that the files be moved according

to the following instructions which may still be used:

• At the C:\> prompt, type “MKDIR QTRACER2” (without the quotes — whenever quotes appear in this

section type the requested information without the quotes).

• Next copy the executable and data files stored in the file Qtr dos on the CD to your hard disk. For

example, you might type (if C is your disk drive): “COPY D:\*.* C:\QTRACER2\*.*.”

• Repeat the above commands for the other files on the CD.

• Put your CD in a safe location.

3If a command prompt is preferred then at the C:\> prompt, type “CD\QTRACER2” without the quotes.

The user will then see a new prompt; C:\QTRACER2>. Assuming the user also copied the necessary data

files or created your own, the user may now type “QTR” to run the program by responding to the requested

information. The user may want to type “QTR filename” such as “QTR QTRACER.D”, which will automatically

load and run the Atkinson data set described in the journal article (Field and Nash, 1997). The user may

do the same with the Mull et al. (1988) data by typing “QTRACER2 MULL.D” to load the appropriate data

files and begin processing.

66
Additional information regarding QTRACER2 execution is presented in Section 7. on

page 90 However, the really important information (files creation) is listed in this section.

6.3. QTRACER2 FUNCTIONING

QTRACER2 runs by processing two types of files at once. The first file processed is a

header file, which identifies the amount of tracer injected into the hydrologic system and

ALL appropriate subfiles. Subfiles are data files, each of which represents a sampling

station where tracer was recovered for the particular study. The subfiles must include all

necessary information for the program to run. They also allow the user to run the program

without interaction with the user (batch mode), pause processing to allow the user to observe

numerical output, and display high-quality graphics. What follows are seven sets of data

files that may be used to test the QTRACER2 program. The data files may also be reviewed

directly, as they are simple ASCII files.

Run QTRACER2 on each of the supplied files and compare the results with the

results provided in the publication “Risk Assessment Methodology for Karst Aquifers:

(1) Estimating Karst Conduit-Flow Parameters” (Field and Nash, 1997) [QTRACER.D and

MULL.D only]. Preferably, you will be able to test the program on your own data sets, where

you may already know the results.

6.4. SAMPLE FILES ON DISK

The following nine “header” data files (*.D) and their respective sample station data files

(*.DAT) are included on the disk (Table 11). Each header file must reference at least one

corresponding sample station data file. However, the number of sample station data files

that correspond to a header file is limited only by your computer’s capabilities.

Note: There is no specific requirement that the data files end with the extensions “D”

or “DAT” (e.g., QTRACER.D; QTRACER.DAT). The “D” and “DAT” extensions are simply

conventions used in this manual and in the example data file.

Descriptions of data files listed in Table 11 follow.

1. QTRACER.D and QTRACER.DAT are hypothetical data sets provided by Dr. Timothy

Atkinson (Atkinson, 1987) for educating students (of which this author was one) on

the proper methodology for analyzing and interpreting BTCs. Analysis of these data

sets using QTRACER2 is presented in considerable detail in Field and Nash (1997).

67
Table 11. Example data files on disk.

Header Data Sample Station

File Data File

QTRACER.D 

MULL.D 

LOST.D 

RCA.D 

TOPLITA.D 

GAR2.D 

MUUL.D 

UVAS281.D 

MOBILE.D 

QTRACER.DAT 

MULL.DAT 

LOST.DAT 

RCA.DAT 

TOPLITA.DAT 

GAR2.DAT 

MUUL.DAT 

UVAS281.DAT 

MOBILE.DAT 

2. MULL.D and MULL.DAT are data sets taken from a U.S. EPA Region IV report (Mull

et al., 1988) in which very comprehensive BTC analysis is described. The MULL.D 

and MULL.DAT data sets appear slightly modified from the original in that data has

been recorded in SI units on the disks. The original Mull et al. data set mixed SI and

English units that QTRACER2 allows for and corrects. Analysis of these data sets

using QTRACER2 is presented in considerable detail in Field and Nash (1997).

3. LOST.D and LOST.DAT are data sets listing the results of a BTC. They were generated

by the senior author (and other students) when Dr. Atkinson was instructing proper

methodology for conducting tracer tests and analyzing and interpreting the results.

It was obtained for the Lost River Cave System in Kentucky.

4. RCA.D and RCA.DAT are the data sets that originally inspired the effort to develop QTRACER2. A tracer test conducted at an RCA del Caribe Superfund site

(Barceloneta, P.R.) supposedly provided substantial information on the functioning

of the karst aquifer and on some solute-transport processes in the aquifer. However,

only about 0.7% of the Cl

− tracer (injected as NaCl) was recovered. Questions regarding the simple calculations and other factors illustrated in Section 4.1. on page 50

of this report warranted a more refined approach. This computer program estimates

recovery at 0.7%, indicating an extremely poor recovery effort at the site.

5. TOPLITA.D and TOPLITA.DAT are modified data sets (Gaspar, 1987a, p. 58) that serve

to demonstrate that an “ideal” BTC is not necessary for QTRACER2 to function

68
properly. The Toplita data sets are also excellent for demonstrating QTRACER2’s

data extrapolation capabilities because of the shape of the curve and the position of

the last measured data point.

6. GAR2.D and GAR2.DAT are modified data sets from a Superfund site in Tennessee.

The original data sets were subjected to extensive data interpolation by the computer

program NDATA (see Section 10.1. on page 154 for a description of NDATA). A

deliberately “huge” data set was constructed to demonstrate QTRACER2’s capability

of handling data sets that are too large for most PCs. The data set also intended to

test the reliability of NDATA’s interpolation capability.

7. MUUL.D and MUUL.DAT are modified data sets of MULL.D and MULL.DAT, respectively.

They were created using NDATA to again assess QTRACER2’s capabilities of handling

“huge” data sets, but with a “variable” discharge (GAR2.DAT has a constant discharge).

8. UVAS281.D and UVAS281.DAT consists of original surface-water tracing data published

by Zand et al. (1976) and republished in Bencala and Walters (1983). It is available

from the U.S. Geological Survey and is provided here to illustrate QTRACER2’s ability

to evaluate surface-water tracing data (see Section 8. on page 115).

9. MOBILE.D and MOBILE.DAT consists of slightly modified data from Molz et al. (1986a,b).

It is reprinted here to illustrate QTRACER2’s ability to evaluate tracer tests conducted in porous media (see Section 8. on page 115).

NOTE: EDIT ONE OF THE *.D FILES AND SAVE AS A NEW FILE WITH A NEW

FILE NAME. THEN EDIT ONE OF THE *.DAT FILES AS OFTEN AS NECESSARY

FOR EACH SAMPLING STATION TO BE ANALYZED. SAVE EACH *.DAT FILE AS

A NEW FILE WITH A NEW FILE NAME.

6.5. DESCRIPTION OF *.D FILES

All descriptions in this section use QTRACER.D as sample input. An example header file,

QTRACER.D, appears in Figure 14.

A *.D file (e.g., QTRACER.D) is very small. A typical *.D file begins with a requestor

for the mass of tracer injected, which should be followed by a value input by the user.

69
QUANTITY OF TRACER INJECTED

450

UNITS OF MEASURE (1-lbs, 2-kg, 3-g, 4-mg)

3

TYPE OF RELEASE AND TIME FOR RELEASE (1-impulse, 2-pulse, 3-step) [HOURS]

1 0.0

TIME FOR TRACER TO REACH FLOW ZONE [HOURS]

0.0

SAMPLING DATA FILES LIST

QTRACER.DAT

Figure 14. QTRACER.D header file for QTRACER2 processing.

Subsequent requestors appear in the same manner as can be seen in Figure 14. That is,

a requestor appears, usually with some options that are allowed, so the user will know

what can be entered, and on the next line the user enters the appropriate response that

QTRACER2 will read. So the first requestor in Figure 14 appears as

QUANTITY OF TRACER INJECTED 

450 

which is simply asking for the quantity of tracer material injected into the system. For

the QTRACER.D example 450 is listed by the user because this was the hypothetical tracer

quantity injected into the system.

The file next requests information on the unit of measure for the tracer mass injected,

because obviously the number 450 has no meaning without any units.

UNITS OF MEASURE (1-lbs, 2-kg, 3-g, 4-mg) 

3 

The numbers enclosed in parentheses represent the valid units allowed by QTRACER2.

The user responds with the appropriate units. For the QTRACER.D example the number 3 is

listed to indicate grams (g) as the unit of measure.

Next is a request for a brief description of the type and time required for tracer injection.

TYPE OF RELEASE AND TIME FOR RELEASE (1-impulse, 2-pulse, 3-step) [HOURS] 

1 0.0 

The numbers enclosed in parentheses represent valid choices for the type of injection used

70
for the tracer test where impulse represents an instantaneous injection, pulse represents

an injection that occurred over some period of measurable time, and step represents a

continuous injection for the length of the tracer test period. The listed units [HOURS] 

is a required entry only for a pulse and step (continuous) releases. An impulse release

demands that the time for release be left blank or set to zero; anything greater than zero

will precipitate QTRACER2 resetting the release time to zero.

The file now requires some entry for the time taken to reach the flow zone. TIME FOR 

TRACER TO REACH FLOW ZONE [HOURS] 

Typically this value will be zero, which must be entered (not left blank) for QTRACER2 to

properly function. The importance of this value is described by Equations (2) and (3) and

 ̄ is used to properly determine t

 ̄, upsilon, and Dxs .

Lastly, the program asks for the name of all subfiles to be called by QTRACER2 for

processing as part of the *.D file. As previously explained, each header file describing the

initial tracer injection conditions must reference at least one sampling station data file,

which will be listed here as *.DAT files (e.g., QTRACER.DAT). The subfiles correspond to

each sampling station at which tracer was recovered.

SAMPLING DATA FILES LIST 

QTRACER.DAT 

For the QTRACER.D example, only one station is listed as having recovered tracer, QTRACER.DAT,

because that is the only station at which this hypothetical trace recovered the tracer.

However, if 23 sampling stations had recovered tracer, then all 23 sample files would

be recorded here — one above the other, but in no particular order. For example, tracer

recovery at 23 sampling stations for the QTRACER.D tracer test might be listed as:

QTRACER.1 

QTRACER.2 

QTRACER.3 ·

·

· QTRACER.23 

Any other appropriate names such as the names of various monitoring wells or monitored

springs are acceptable. The only requirement is that the user be able to recognize the names

after QTRACER2 has been run, as it is most advantageous to run QTRACER2 in batch

mode for large data sets.

71

0.0 
6.6. DESCRIPTION OF *.DAT FILES

All descriptions in this section use QTRACER.DAT as sample input except as otherwise listed.

An example sampling station data file, QTRACER.DAT, appears in Figure 15.

The *.DAT files (e.g., QTRACER.DAT) are fairly long and detailed. They must be detailed

so that the program can properly process all the necessary site information.

6.6.1. Sampling Frequency

A *.DAT file begins by requesting the units used for listing the time data, which must

be consistent. The actual time data are listed at the very end of this file along with the

concentration data and discharge data when appropriate. The first item for a *.DAT file is

SAMPLING FREQUENCY: UNITS (1=days, 2=hrs, 3=min, 4=sec) 

2 

in which a value of 2 is listed because time was recorded in hours.

NOTE: SAMPLING FREQUENCY does NOT mean that there must be an even time span

between sampling events, only consistent units.

6.6.2. Tracer Mass Recovery

The tracer recovery data must also have consistent units, which follows the same convention

as sampling frequency.

TRACER RECOVERY CONCENTRATION: UNITS (1=g/L, 2=mg/L, 3=ug/L, 4=ng/L) 

3 

So for the QTRACER.DAT example, 3 was recorded because tracer concentration is recorded

at the end of this file (corresponding to time data) in units of μg L−1.

6.6.3. Flag for Background

Quite commonly, a background concentration value is measured prior to initiating a tracer

test. This value must be subtracted from the measured concentration values to allow for a

more accurate mass balance estimation.

FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) [VALUE] 

0 

The word “FLAG” is a marker that acts like an on/off switch. It informs QTRACER2 how

to respond. The number 0 for the QTRACER.DAT data set tells QTRACER2 that no value

for background is available — no “value” is required. The number 1 tells QTRACER2 that

a background value is available for subtracting from the data set — a number 1 MUST be

72
SAMPLING FREQUENCY: UNITS (1=days, 2=hrs, 3=min, 4=sec)

2

TRACER RECOVERY CONCENTRATION: UNITS (1=g/L, 2=mg/L, 3=ug/L, 4=ng/L)

3

FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) AND [VALUE]

00

DISCHARGE IN DATA FILE OR CONSTANT: (1=data file, 2=constant)

1

DISCHARGE: UNITS (1=m^3/d, 2=m^3/hr, 3=m^3/min, 4=m^3/sec, 5=gpd, 6=gpm,

7=ft^3/d, 8=ft^3/hr, 9=ft^3/min, 10=ft^3/sec) [VALUE] 

40 

ESTIMATE SYSTEM VOLUME (1=yes, 0=no) 

1 

RADIAL DISTANCE TO SAMPLING STATION: UNITS (1=m, 2=ft, 3=km, 4=miles) [VALUE] 

3 1.8 

CORRECTION FOR SINUOSITY (1=yes, 0=no) [VALUE, def=1.0] 

1 1.5 

FLOW MEDIUM: POROSITY (1=subsurface channel, 2=surface channel, 

3=porous medium, 4=fractured medium) [VALUE, def=1.0] 

1 1.0 

IF POROUS FLOW: UNITS, HYDR. COND. (1=m/s, 2=m/hr, 3=ft/s, 4=m/hr, 0=null) 

IF FRACTURE(S) FLOW: UNITS, HEIGHT (1=m, 2=ft, 0=null) [VALUE] 

0 0.0 

NAME OF THE FILE OF INPUT/OUTPUT VALUES 

Q1.OUT 

INTERPOLATE DATA (1=yes, 0=no) [NUMBER OF KNOTS] 

0 1000 

NAME OF THE INTERPOLATED OUTPUT VALUES FILE 

Q1.INT 

Figure 15. QTRACER.DAT sampling station data file for QTRACER2 processing.

73
EXTRAPOLATE DATA (1=yes, 0=no) [1=EXP. DECAY, 2=CUBIC HERMITE, 3=STAT. METH.]

01

VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)

0 1 10

VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT)

0 1 10

VISUALIZATION: CHATWIN PARAMETERS (CHECK PRINT PLOT OPLOT)

0 0 10

FLAG FOR FILE OF DATA FOR CXTFIT MODELING (CXTFIT Min Mout)

0 0 0

NAME OF FILE FOR SOLUTE-TRANSPORT MODELING (VALID IF FLAG=1)

C:\VANGENU\CXT\Q1.ADV

FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0)

1

NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1)

Q1.NRM

VISUALIZATION: NORMALIZED CONCENTRATION (CHECK PLOT JOIN OPLOT)

0 0 10

FLAG FOR NORMALIZED TRACER LOAD FILE (1/0)

1

NAME OF FILE FOR NORMALIZED TRACER LOAD VALUES (VALID IF FLAG=1)

Q1.LOD

VISUALIZATION: NORMALIZED TRACER LOAD (CHECK PLOT JOIN OPLOT)

0 0 10

FLAG FOR STANDARDIZED TIME AND CONCENTRATION VALUES FILE (1/0)

1

NAME OF FILE FOR STANDARDIZED TIME AND CONCENTRATION (VALID IF FLAG=1)

Q1.STN

VISUALIZATION: STANDARDIZED TIME AND CONCENTRATION (CHECK PLOT JOIN OPLOT)

0 0 10

Figure 15. QTRACER.DAT sampling station data file for QTRACER2 processing (continued).

74
FLAG FOR OUTPUT TO SCREEN AND PAUSE AS NECESSARY (1/0)

1

FLAG FOR DATA ANALYSIS METHOD (1,ALL DATA; 2,BLOCK AVE; 3,BLOCK SKIP)

3

TIME CONCENTRATION DISCHARGE (CONDITIONAL)

0.0 0.00 4.10

1.0 0.00 4.20

2.0 0.00 4.27

3.0 0.00 4.35

4.0 0.00 4.42

5.0 0.00 4.50

6.0 0.00 4.57

7.0 6.50 4.67

8.0 7.50 4.75

9.0 4.60 4.82

10.0 2.10 4.90

11.0 1.10 4.80

12.0 0.93 4.68

13.0 0.88 4.56

14.0 0.83 4.46

15.0 0.75 4.33

16.0 0.63 4.22

17.0 0.40 4.12

18.0 0.18 4.00

19.0 0.08 3.90

20.0 0.03 3.80

Figure 15. QTRACER.DAT sampling station data file for QTRACER2 processing (continued).

75
followed by a number [VALUE] (i.e., concentration) in the SAME units as those in which

the concentration data set is recorded.

The [VALUE] is a requestor that applies only when the FLAG isset to 1,in whi ch

case the user MUST supply a background concentration for subtraction from the measured

concentration values. The user is asked to supply a number only if appropriate. However,

this number may be zero.

For example, in the MULL.DAT example, the flag for background appears as

FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) [VALUE] 

1 0.01 

because a background tracer concentration of 0.01 μg L−1 is available. This value will

automatically be subtracted from all concentration values in the time-concentration data

file prior to processing (but after data interpolation and/or extrapolation). Note that the

MULL.DAT data set has already been identified as having tracer recovery concentration values

recorded in units equal to μg L−1.

6.6.4. Measured Discharge

Discharge is typically measured as a single occurrence during a tracer test and taken as a

constant value, or measured periodically throughout the tracing experiment. QTRACER2

needs to know which way discharge was measured for proper processing.

DISCHARGE IN DATA FILE OR CONSTANT: (1=data file, 2=constant) 

means that for 1=data file, the time-concentration listing at the end of the *.DAT file must

also contain a third column of discharge values. The 2=constant means that discharge is a

constant, the value for which must be included in the next section with the discharge units

of measure. So for the QTRACER.DAT file, a variable discharge 1 is listed, which means that

there MUST be a third column of data at the end of the QTRACER.DAT data file (Figure 15).

If a single (e.g., constant) discharge was recorded, then the user would enter 2 on the

appropriate line.

6.6.5. Discharge Units

As with all the other data listed, QTRACER2 needs to know in which units discharge was

measured so that an appropriate correction to allow for consistent units can be made. A

considerable range of discharge unit measures is allowed by QTRACER2, so the requestor

actually takes up two lines in the data file.

76

1 
DISCHARGE: UNITS (1=m^3/d, 2=m^3/hr, 3=m^3/min, 4=m^3/sec, 5=gpd, 6=gpm, 

7=ft^3/d, 8=ft^3/hr, 9=ft^3/min, 10=ft^3/sec) [VALUE] 

4

A number 4 by itself indicates that a variable discharge is recorded in m^3/sec (m3 s−1), the

values for which are listed at the end of the data file (QTRACER.DAT). (QTRACER2 converts

all other discharge choices to m3 s−1 prior to processing the file.)

If a constant discharge is to be used (e.g., LOST.DAT) then the user would record

DISCHARGE: UNITS (1=m^3/d, 2=m^3/hr, 3=m^3/min, 4=m^3/sec, 5=gpd, 6=gpm, 

7=ft^3/d, 8=ft^3/hr, 9=ft^3/min, 10=ft^3/sec) [VALUE] 

4 1.78

to indicate that a constant discharge in m^3/sec (m3 s−1) with a value of 1.78 isto be used

in the analysis.

If sampling was performed at a nonpumping well by withdrawing an aliquot of water

from the well by use of a bailer, then discharge is unknown (although there is clearly some

flux of water flowing past the well). The user should enter a very small flux value unless

the flux can be guessed. For example, the user might enter:

DISCHARGE: UNITS (1=m^3/d, 2=m^3/hr, 3=m^3/min, 4=m^3/sec, 5=gpd, 6=gpm, 

7=ft^3/d, 8=ft^3/hr, 9=ft^3/min, 10=ft^3/sec) [VALUE] 

4 1.0E-10

By entering “4 1.0E-10” (entering the value 4, a blank space, and then 1.0E-10) into the

program, the user is multiplying the tracer concentration data file by a very small value

so a minimal effect might be applied assuming very little flux past the well (e.g., for tight

fissures). Mathematically this works; physically, this suggests that discharge is known and

is negligible, which may not be correct and may create a fairly substantial error in data

analysis.

6.6.6. System Volume

The system volume can be estimated by QTRACER2 provided the time-concentration data

file begins at zero time. (QTRACER2 now automatically adds zero time when zero time is

absent from the time-concentration data file.) A simple on/off switch informs QTRACER2

to estimate volume. If the switched is set to off, then subsequent geometries (e.g., crosssectional area) will also not be estimated.

ESTIMATE SYSTEM VOLUME (1=yes, 0=no) 

1 

The switch value 1 for the QTRACER.DAT example informs QTRACER2 that system volume

should be estimated.

77
6.6.7. Radial Distance

QTRACER2 needs to know the straight-line distance to the sampling station from the injection site and the units by which distance was measured.

RADIAL DISTANCE TO SAMPLING STATION: UNITS (1=m, 2=ft, 3=km, 4=miles) [VALUE] 

3 1.8 

A distance equal to 1.8 kilometers is entered for the QTRACER.DAT example.

6.6.8. Correction for Sinuosity

Because most solution conduits and fractures are not straight-line features, a sinuosity factor

may be included for QTRACER2 to use in processing the data.

CORRECTION FOR SINUOSITY (1=yes, 0=no) [VALUE, def=1.0] 

1 1.5 

A li sti ng of 1 1.5 tells QTRACER2 to correct the radial distance for sinuosity by a factor

of 1.5×. However, if no value is listed, a default equal to 1.0 is supplied. The sinuosity

factor is limited to a range of 1.0 ≤ 3.0.

6.6.9. Flow Medium

QTRACER2 allows the user to decide if the flow system conforms to a subsurface channel

such as a typical karst solution-conduit or mine tunnel (e.g., tubular), surface channel

such as a small stream or large river (e.g., Missouri River), porous medium (e.g., granular

aquifer), or fracture opening (e.g., planar) or set of fractures. If it is a fractured-rock system,

a porosity value will need to be entered by the user as per the VALUE request. A default

of 1.0 (100%) porosity is used if no value is listed, which suggests that all flow occurred

via a single fracture. A porosity value has no effect for flow through subsurface channels

or surface channels. A porosity value also has no effect on a porous-media flow system in

QTRACER2 if a hydraulic conductivity value is missing.

FLOW MEDIUM: POROSITY (1=subsurface channel, 2=surface channel, 

3=porous medium, 4=fractured medium) [VALUE, def=1.0] 

For QTRACER.DAT, a value of 1 tells QTRACER2 to consider subsurface-channel flow only;

a porosity value does not need to be entered because QTRACER2 automatically sets a

default value of 1.0.

78

1 
6.6.10. Porous-Media and Fracture Units

If tracer migrated through a porous medium, then the user would list the estimated

hydraulic conductivity by first recording a units identifier (e.g., 1) and then an actual

value representing the hydraulic conductivity.

Alternatively, if the tracer migrated through a fractured-rock system, then the user

would list the fracture(s) measured or estimated height units. Otherwise, QTRACER2 will

do its best to estimate the height, although the estimated value may not be very reliable.

IF POROUS FLOW: UNITS, HYDR. COND. (1=m/s, 2=m/hr, 3=ft/s, 4=m/hr, 0=null) 

IF FRACTURE(S) FLOW: UNITS, HEIGHT (1=m, 2=ft, 0=null) [VALUE] 

0 0.0

The flag 0 is irrelevant here because flow is a subsurface channel. However, for porous media

or fracture flow, the flag 0 tells QTRACER2 that fracture height is unknown and must be

estimated by QTRACER2.

6.6.11. Output File Name

QTRACER2 requires that an output filename be given so that the results may be written

to an “output file.” The requestor is listed as INPUT/OUTPUT because much of the output

information is a repeat of input information.

NAME OF THE FILE OF INPUT/OUTPUT VALUES 

Q1.OUT 

The output file name Q1.OUT is used here because it allows for easy deletion without

inadvertently deleting the original input files. Any filename is allowed by QTRACER2,

although the user may not want to use a name that is excessively long.

6.6.12. Sample Data Interpolation

QTRACER2 is very good at data interpolation. It relies on a piecewise cubic Hermite to

determine the best possible interpolant for the given data.

INTERPOLATE DATA (1=yes, 0=no) and [NUMBER OF KNOTS] 

This requestor is asking if the user would like to interpolate the data. A 0 means NO and the

user may move on. A 1 (QTRACER.DAT example) means YES and the user then must inform

QTRACER2 of the MINIMUM number of knot points to be created by the interpolation

algorithm.

To create an interpolated data file, the user might record the following.

INTERPOLATE DATA (1=yes, 0=no) and [NUMBER OF KNOTS] 

79

0 
1 200

The flag and value 1 200, respectively, inform QTRACER2 that data interpolation is desired

and that ≥ 200 knots points (interpolated data points) are required. Any value other than

200 could be used as computer memory allows.

6.6.13. Interpolated Data File Name

If an interpolated data file is to be created for processing, it must be given a name. This

file is then stored and can be viewed later or deleted as desired.

NAME OF THE INTERPOLATED OUTPUT VALUES FILE 

Q1.INT 

The output filename Q1.INT is used here because it allows for easy deletion without

inadvertently deleting the original input files. Any file name is allowed by QTRACER2,

although the user may not want to use a name that is excessively long. If data interpolation

is not requested above, this requestor is ignored by QTRACER2.

6.6.14. Sample Data Extrapolation

QTRACER2 is also very good at data extrapolation, but it is up to the user to determine

the method preferred. That is, the user must decide if an exponential decay function, a

piecewise cubic Hermite, or a straight-line projection from the last peak value through the

descending limb is most reasonable. Data extrapolation requires that the peak tracer concentration be obtained and that the descending limb of the breakthrough curve be started.

EXTRAPOLATE DATA (1=yes, 0=no) [1=EXP. DECAY, 2=CUBIC HERMITE, 3=STAT. METH.] 

The 01 means that no extrapolation for the QTRACER.DAT file is requested (the second flag,

1, has no effect in this instance).

A 1=EXP. DECAY means that data extrapolation will be an exponential decay function,

a 2=CUBIC HERMITE means that data extrapolation will be by means of a piecewise cubic

Hermite, and a 3=STAT. METH. means that data extrapolation will be by the statistical

method of projecting lines from the peak concentration through the late-time data onto the

x axis and determining the greatest cluster.

QTRACER2 allows the user to extrapolate data to zero or near zero concentration (after

subtracting any background tracer concentration) without data interpolation. The user will

know the extent of data extrapolation by (1) examining the interpolation data file created

if the interpolation flag is switched on, or (2) by simply observing the “upper limit” to

80

01 
integration displayed at the top of the final output screen/file. The latter can be observed

whether a data interpolation file has been created or not.

6.6.15. Visualize Original Data

The original data may be visually examined before full processing by the user (CHECK),

plotted as points (PLOT), joined by a line (JOIN), and directly sent as a PostScript plot to

a file for later printing (OPLOT). Any one of these four items may be requested or not as

desired.

VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)

0 1 10

The requestors CHECK PLOT JOIN OPLOT are asking if the user would like to:

1. Examine the concentration data file (CHECK).

2. Plot the data on the screen (PLOT).

3. Draw a smooth line through the data points (JOIN).

4. Automatically create a PostScript output file for plotting (OPLOT).

A number 1 answers YES to a requestor, a number 0 answers NO to a requestor. So for the

QTRACER.DAT example:

VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)

0 1 10 

tells the program to:

1. Not show the data file (CHECK = 0).

2. Plot the data on the screen (PLOT = 1).

3. Draw a smooth curve through all the points (JOIN = 1).

4. Not create a PostScript output file automatically (OPLOT = 0).

Data Plotting Each individual plot screen allows for considerable interactive graphics

so that the user may customize the plots as desired. The interactive graphics are explained

in Section 5.6.1. on page 61 using the pull-down menus.

Sometimes the curve may look somewhat odd; this occurs because the interpolation

algorithm used for smooth plotting sometimes has difficulty jumping to oddly placed data

81
points4. Data interpolation by QTRACER2 will help overcome this effect. Also, fewer than

three data points will result in no data smoothing.

More importantly, the shape of the curve drawn through the data points does not

necessarily represent the integration. QTRACER2 will perform a much better integration of

the curve than appears on the screen, in that it will seamlessly connect the points smoothly

even though this function cannot be observed by the user. So the user need not be troubled

by the smooth line drawn on screen not appearing to be entirely “perfect.”

Automatic Postscript Files Automatic PostScript file creation of the plot files is very

advantageous when numerous data files must be processed as a batch operation. However,

these files will not be produced if the program is set to NOT create a file. This item will

usually be set to zero except when QTRACER2 is run in batch mode, because the PostScript

files can be quite large and printing them is unnecessary until a final version based on user

modifications is desired.

Using QTRACER2 for automatic PostScript output does NOT REQUIRE that the

data filenames be shorter than six characters. For the initial data file, the new name

adds underscores and extensions as appropriate. For example, the Qtracer.dat data file

would result in a PostScript plot file named Qtracer dat.ps to identify it as a plot of

the actual data file as recorded by the user. Likewise, an interpolated data file would

be named Qtracer int.ps and a Chatwin data file would be named Qtracer cht.ps. However,

all subsequent PostScript plot data file would conform to user chosen output file names. For

example, a normalized tracer mass file would be named Q1 nrm.ps.

Manual Bitmapped Files Bitmapped files of all screen plots can be created very easily

by QTRACER2. These will usually be done when QTRACER2 is not being run in batch

mode. This is accomplished using the File pull-down menu described in Section 5.6.1. on

page 61

6.6.16. Visualize Interpolated Data

This requestor is used in the same manner as the previous visualization requestor. The only

difference is that it deals with interpolated data only. It functions when data interpolation

4This problem was evident in Version 1.0 of QTRACER mainly due to the bezier algorithm used for

data smoothing. Version 2 of QTRACER (QTRACER2) does not exhibit this problem so readily because

the bezier algorithm has been replaced by a cubic Hermite algorithm.

82
was requested by the user.

VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT) 

0 1 10 

This example 0 1 10 tells QTRACER2 to do nothing for the QTRACER.DAT data file

because no data interpolation was requested. If interpolation data had been requested,

then 0 1 10 would tell QTRACER2 to not display the interpolated data, plot the data

with a line on screen, and not produce a PostScript plot file.

6.6.17. Visualize Chatwin Parameters

For longitudinal dispersion estimation, QTRACER2 will first attempt the Chatwin method.

If the storage arrays are exceeded, it will go to the method of moments.

The Chatwin parameters are visualized in the same manner as the previous items except

for connecting the data points with a line. That is, the Chatwin parameters may be

examined (CHECK), printed to a file (PRINT), plotted (PLOT), and sent to a file as a PostScript

plot file (OPLOT). There is no JOIN function because the Chatwin method automatically relies

on fitting a straight line through the early-time data.

VISUALIZATION: CHATWIN PARAMETERS (CHECK PRINT PLOT OPLOT) 

0 0 10 

The switches, 0 0 10 for the QTRACER.DAT example, inform QTRACER2 that the data is

to be plotted on the screen only.

6.6.18. CXTFIT2.0 Data File Creation

In some instances, it is possible and desirable to use CXTFIT2.0 (Toride et al., 1995) to

model the data. QTRACER2 facilitates this by allowing the user to automatically create

an input file for use with CXTFIT2.0.

Form of CXTFIT2.0 File This option allows the user to request creation of a CXTFIT

file (CXTFIT) and use the original injected tracer mass (Min) or the recovered tracer mass

(Mout) for processing. Determining whether to use the mass injected or the mass recovered

is more than just a preference item. It is related to the functioning of the system and the

number of recovery stations (e.g., more than one recovery station will usually require Mout),

and greatly affects mass balances.

FLAG FOR FILE OF DATA FOR CXTFIT MODELING (CXTFIT Min Mout)

0 0 0

The three switches 0 0 0 tell QTRACER2 not to create a CXTFIT2.0 file and not to use

83
either the mass injected or mass recovered in file creation. If a CXTFIT2.0 file option was

set to 1 and the other two options set to 0, then a default of mass injected (Min) would be

used.

If a CXTFIT2.0 file is to be created for use in the CXTFIT2.0 model, then the user

should:

1. Obtain a copy of the program and the user’s manual. CXTFIT2.0 is a very complicated

program and requires considerable reading of the manual to understand its functioning.

2. IGNORE all FIRST line data after the first item of the CXTFIT2.0 created file —

QTRACER2 adds some additional information for user examination that is not read

by CXTFIT2.0.

3. QUESTION initial values for the selected parameters. For example, if QTRACER2

was forced to use the method of moments to estimate dispersion, then the “D”

parameter listed in the CXTFIT2.0 created file could be too large for a global minimum

to be found.

These three items are essential before embarking on the use of CXTFIT2.0.

CXTFIT File Name and Location If a CXTFIT2.0 input file is to be created, then

the user must give the file a name. Also, if the CXTFIT2.0 program is not stored in the

same location as QTRACER2, then it is desirable to give it a path to where it should be

created so that the user will not need to type in the path to the CXTFIT2.0 file.

NAME OF FILE FOR SOLUTE-TRANSPORT MODELING (VALID IF FLAG=1) 

C:\VANGENU\CXT\Q1.ADV 

The data line, C:\VANGENU\CXT\Q1.ADV, tells QTRACER2 to create the CXTFIT2.0 file at

the above listed path where the executable version of CXTFIT2.0 is stored. Actually, the

requestor is ignored in this instance because QTRACER2 was informed above not to create

a CXTFIT2.0 file.

Any of the files that QTRACER2 creates (except as by OPLOT) can be given a path for

file storage.

6.6.19. Normalized Tracer Concentration

The time-concentration data may be normalized for mass according to the Mull et al. (1988)

method. That is, the concentration data may be rewritten into consistent units (mg L−1)

84
kg−1 injected to allow for comparison of multiple BTCs conducted at the same tracer

injection-recovery location. This newly created data may also be examined.

Flag to Create Normalized Data File for Mass The creation of a normalized

concentration data file is performed by the on/off switch described earlier (1=on, 0=off).

FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0) 

1 

Name of Normalized Concentration File for Mass As with all other files created

by QTRACER2, a filename must be provided before QTRACER2 can create the file.

NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1) 

Q1.NRM 

A filename with an extension (*.NRM) is not required. Any name is acceptable. The “VALID

IF FLAG=1” requestor refers to the above on/off switch.

Visualize Normalized Concentration The newly created normalized concentration

file can be visualized in the same manner as the original data. That is, the data can be

examined (CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to a

file in PostScript form for PostScript plotting (OPLOT).

VISUALIZATION: NORMALIZED CONCENTRATION (CHECK PLOT JOIN OPLOT)

0 0 10 

Setting the four switches to 0 0 10 tells QTRACER2 to display a smooth line on the

screen.

6.6.20. Normalized Tracer Load

The tracer concentration data may be normalized for loading according to the Mull et 

al. (1988) method. That is, the concentration data may be rewritten into consistent units

of (mg s−1) kg−1 injected to allow for comparison of multiple BTCs conducted at the same

tracer injection-recovery location. This newly created data may also be examined.

Flag to Create Normalized Data File for Loading The creation of a normalized

concentration data file is again performed by the on/off switch described earlier (1=on,

0=off).

FLAG FOR NORMALIZED TRACER LOAD FILE (1/0)

1 

85
Name of Normalized Concentration File for Load As with all other files created

by QTRACER2, a filename must be provided before QTRACER2 can create the file.

NAME OF FILE FOR NORMALIZED TRACER LOAD VALUES (VALID IF FLAG=1) 

Q1.LOD 

A filename with an extension (*.LOD) is not required. Any name is acceptable.

Visualize Normalized Tracer Load The newly created normalized load file can be

visualized in the same manner as the original data. That is, the data can be examined

(CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to a file in

PostScript form for PostScript plotting (OPLOT).

VISUALIZATION: NORMALIZED TRACER LOAD (CHECK PLOT JOIN OPLOT)

0 0 10 

Setting the four switches to 0 0 10 tells QTRACER2 to display a smooth line on the

screen.

6.6.21. Standardized Data File

The tracer concentration data may be standardized for dimensionless time and concentration

according to the Mull et al. (1988) method. That is, time may be rewritten by

(t − t

 ̄) (70)

σt

and concentration data may be rewritten by

C (71) Cp

to create a completely dimensionless tracer-recovery curve that may be used as a “type

curve” for future contaminant release problems (see Mull et al. [1988] for a comprehensive

discussion). This newly created data may also be examined.

Breakthrough curves generated by multiple tracer tests conducted from the same

tracer-release point to the same tracer-recovery point conducted under differing hyrdologic

conditions may be examined by plotting each standardized BTC on the same graph. When

comparing the BTCs, it is useful to note the skewness and kurtosis (see Section 3.3.

on page 32) as well as visually noting similarities in the curves of each BTC. Apparent

differences between plotted BTCs, skewness, and/or kurtosis must be critically examined

to determine if the differences may be judged significant.

86
Flag to Create Standardized Data File The creation of a standardized dimensionless

data file is again performed by the on/off switch described earlier (1=on, 0=off).

FLAG FOR STANDARDIZED TIME AND CONCENTRATION VALUES FILE (1/0) 

1 

Name of Standardized Data File As with all other files created by QTRACER2, a

filename must be provided before QTRACER2 can create the file.

NAME OF FILE FOR STANDARDIZED TIME AND CONCENTRATION (VALID IF FLAG=1) 

Q1.STN 

A filename with an extension (*.STN) is not required. Any name is acceptable.

Visualize Standardized Data File The newly created standardized time-concentration file can be visualized in the same manner as the original data. That is, the data can

be examined (CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to

a file in PostScript form for PostScript plotting (OPLOT).

VISUALIZATION: STANDARDIZED TIME AND CONCENTRATION (CHECK PLOT JOIN OPLOT)

0 0 10 

Setting the four switches to 0 0 10 tells QTRACER2 to display a smooth line on the

screen.

6.6.22. Screen Display

QTRACER2 allows for processing interruption for displaying results by use of the on/off

switch (1=on, 0=off). If the user would like to view the program results as they become

available, then the switch should be set to 1=on. QTRACER2 will pause periodically to

allow the user to view the results; RETURN will inform QTRACER2 to continue.

Setting the switch to 0=off allows QTRACER2 to run in the batch mode. This is

preferable when many sample station data files must be processed for a single header file.

FLAG FOR OUTPUT TO SCREEN AND PAUSE AS NECESSARY (1/0) 

1 

6.6.23. Method for Handling Large Time-Concentration Data Files

With the advent of automatic data loggers, incredibly large time-concentration data files

are being recorded. Often these files are much too large for conventional computer memory

allocation. Because of this problem, QTRACER2 has been programmed to allow for

adjustment accordingly by:

87
1. Using all the time-concentration data, provided computer memory is not exceeded.

2. Averaging blocks of data to create a single data point for each block.

3. Skipping blocks of data.

The more measured data that QTRACER2 can handle the better. Therefore, if QTRACER2

must use less than all the data it will attempt to minimize the size of the blocks it must

average or skip.

FLAG FOR DATA ANALYSIS METHOD (1,ALL DATA; 2,BLOCK AVE; 3,BLOCK SKIP) 

1 

Two sets of data files were created to be “huge” are included on the disk. The first set,

GAR2.D and GAR2.DAT, were created by interpolation data collected at a Superfund site with

constant discharge. The second set, MUUL.D and MUUL.DAT, was created from the MULL

data set by interpolation and include a “variable” discharge (although discharge did not

always vary while being measured).

6.6.24. Actual Time-Concentration Data

The last item to be listed for each *.DAT file is the actual time-concentration data and

discharge data if these were not constant. The actual time-concentration data set (and

discharge data, if relevant) are recorded in the UNITS identified at the top of the *.DAT

file. Discharge must only be listed if a variable discharge was measured at each sampling

interval. For the QTRACER.DAT example:

TIME CONCENTRATION DISCHARGE (CONDITIONAL)

0.0 0.00 4.10 .

.

.

20.0 0.03 3.80

is listed to correspond with TIME CONCENTRATION DISCHARGE measurements. The parenthetical CONDITIONAL relates to whether discharge was variable or constant. If discharge

was earlier identified as a variable, then a discharge column must be recorded; if discharge

was earlier identified as a constant, then a discharge column must not appear.

If a single or average (constant) discharge was measured for the site, a constant discharge

value should have been identified earlier in the data file where appropriate. So for the

RCA.DAT example, only the TIME CONCENTRATION values are recorded as:

88
TIME CONCENTRATION DISCHARGE (CONDITIONAL) 

0.0 0.0 

.

.

.

24.0 6.0 

Earlier in the RCA.DAT data file (near the top), discharge had been identified as being a

CONSTANT (flag = 2) wi th UNITS and VALUE equal:

66 

which indicates that discharge was recorded in “gpm” (flag = 6) and the actual discharge

value is 6 (the second 6 listed).

Be advised that the TIME CONCENTRATION files do not need to list all the occurrences

of zero tracer recovery at the beginning of the tracer study. However, the time 0.0 should

be listed at the very top of the data file to indicate the time of tracer injection. If system

volumes are to be estimated for a variable discharge, TIME must begin with 0.0. As noted

above, zero time is now automatically added when missing from the time-concentration data

file.

Conduit volume and Reynolds number can only be calculated if discharge is measured

at a SPRING, not a well. If a well is analyzed and the appropriate flags turned on to

indicate a desire to calculate conduit volume and Reynolds number, both will be calculated,

but significant uncertainties should be expected in the results, making calculations for the

RCA.DAT data sets suspect.

89
7. EXAMPLE ANALYSES FROM QTRACER2

QTRACER2 is very easy and fast to use once the necessary header file and sampling station

data files have been created (see Section 6. on page 65). As described in Section 6.2. on

page 66, the user need only place the pointer on the QTR icon and Left Double-Click 

to initiate QTRACER2, which introduces the program and prompts for the name of a

header file (tracing project file). At this point the user may type any valid header filename

(e.g., Qtracer.D) or just press <Enter> to automatically run the QTRACER2 default file

(Qtracer.D) and observe proper functioning of QTRACER2.

At this point, QTRACER2 will proceed until finished if the batch mode has been

specified (see Section 6.6.22. on page 87). Alternatively, if the user requested screen display,

QTRACER2 will pause periodically to allow the user to observe the analytical results as

they become available. Simply pressing <ENTER> as directed by QTRACER2 will cause

QTRACER2 to move to the next available display screen except for the data plot screens.

The plot screens require the user to click the Left Click anywhere on any particular child

window to highlight that window for interactive manipulation using the pull-down menus

and for viewing. Left Clicking on the Graphic1 screen returns the user to the data-display

screen.

Lastly, if multiple sampling station data files are to be processed by QTRACER2 for

a single tracing project file or header file (see Section 6.5. on page 69), then QTRACER2

will enter a loop mode. Upon completion of processing a single sampling station data file,

QTRACER2 will clear most of its memory and loop back to read and process the next

sequentially listed sampling station data file in the header file list. Upon processing all

the sampling station data files, QTRACER2 will then develop a final total output of some

specific information (e.g., total mass recovery) and append this small output subfile to the

LAST specified sampling station output file.

7.1. QTRACER.D EXAMPLE OUTPUT

In Section 6.5. on page 69 QTRACER.D was used as a sample tracing project file or header file.

QTRACER.D referenced the sampling station data file, QTRACER.DAT (Section 6.6. on page 72,

and Table 11), that provided all the information necessary for QTRACER2 processing of

the data for that sampling station.

90
7.1.1. QTRACER.DAT Tracer-Breakthrough Curve

Figure 16 depicts the basic tracer-breakthrough curve generated and analyzed by QTRACER2.

Note that discharge was measured each time a water sample was collected.

7.1.2. QTRACER.DAT Chatwin Plot

Figure 17 depicts the data plot and straight-line fit of the Chatwin parameter for longitudinal

dispersion generated and analyzed by QTRACER2. Note that the equation for the straightline and the relevant statistics describing the straight-line fit were generated by QTRACER2

where Y = 747.901 + -95.3754 is of the form y = mx + b and Equations (41) and (42) are:

x1 = 747.901 and x2 = −95.3754.

7.1.3. QTRACER.DAT Output File

Figure 18 depicts the final analytical output generated by QTRACER2. Besides observing

the analytical results, note the end of the output file, which depicts the complete results

of the analysis. QTRACER2 performs this function even though only a single sampling

station data file was analyzed. As such, the total results are the same as those listed in the

main part of the output file.

7.1.4. QTRACER.DAT Normalized Tracer Concentration

Figure 19 depicts the normalized tracer concentration data generated by QTRACER2

according to the method described by Mull et al. (1988). Note the concentration units

for the y axis.

7.1.5. QTRACER.DAT Normalized Tracer Load

Figure 20 depicts the normalized tracer load data generated by QTRACER2 according to

the method described by Mull et al. (1988). Note the concentration units for the y axis.

7.1.6. QTRACER.DAT Standardized Time-Concentration Data

Figure 21 depicts the standardized-time concentration data generated by QTRACER2

according to the method described by Mull et al. (1988). Note the time units on the x

axis and the concentration units on the y axis.

91
Figure 16. Tracer-breakthrough curve for the QTRACER.DAT sampling station data file.

92
Figure 17. Plot and straight-line fit of the Chatwin parameter for the QTRACER.DAT sampling

station data file.

93
******************************************************************** 

* * 

* Listing of output for: QTRACER.DAT * 

* * 

******************************************************************** 

Limits to integration for the data file: QTRACER.DAT 

Lower integration limit .00000 hrs 

Upper integration limit 20.000 hrs 

The quantity of tracer recovered.44798 kg 

447.98 g 

.44798E+06 mg 

.44798E+09 ug 

Distance from input to outflow point 2.7000 km 

Corrected for sinuosity = 1.50X 

Time to leading edge (first arrival) 7.0000 hrs 

Time to peak tracer concentration 8.0000 hrs 

For a peak tracer concentration 7.5000 ug/L 

Figure 18. Output file for the QTRACER.DAT sampling station data file.

94
The mean tracer transit time

.38629 d 

9.2711 hrs 

556.26 min 

Variance for mean tracer time.11515E-01 d^2 

6.6325 hrs^2 

23877. min^2 

Standard deviation for tracer time.10731 d 

2.5754 hrs 

154.52 min 

The mean tracer velocity6989.5 m/d 

291.23 m/hr 

.80897E-01 m/s 

Standard deviation for tracer velocity1637.7 m/d 

68.238 m/hr 

.18955E-01 m/s 

Dispersion coefficient 3.2582 m^2/s 

Longitudinal dispersivity 40.276 m 

Peclet number67.037 

Advection > Diffusion 

Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).

95
The maximum tracer velocity

9257.1 m/d 

385.71 m/hr 

.10714 m/s 

Flow-channel volume estimate .14941E+06 m^3 

Based on a lower integration limit .00000 hrs 

and on an upper integration limit 9.2711 hrs 

Flow-channel cross-sectional area 55.338 m^2 

Flow-channel surface area .51674E+08 m^2 

Tracer sorption coefficient (channel) .13016E-04 m 

Hydraulic head loss along channel .12078E-01 m 

Based on a friction factor .11254 

Viscous-flow sublayer along walls 1.3779 mm 

Estimated Reynolds number .59564E+06 

Based on an estimated tube diameter 8.3939 m 

Estimated Froude number .10061E-01 

Based on an estimated hydraulic depth 6.5926 m 

Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).

96
Molecular mass transport parameters 

Shear velocity .17006E-01 m/s 

Estimated Schmidt number 1140.0 

Estimated Sherwood number 14926. 

Mass transfer coef. from wall to flow .17782E-05 m/s 

Molecular diffusion layer thickness .56238 mm 

Percent recovery of tracer injected 99.552 % 

Accuracy index (0.0 = Perfect Recov.) .4481E-02 

Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).

97
******************************************************************** 

* * 

* Listing of output for: QTRACER.DAT * 

* * 

******************************************************************** 

Total quantity of tracer recovered.44798 kg 

447.98 g 

Total aquifer volume estimate .14941E+06 m^3 

Total aquifer surface area estimate .51674E+08 m 

Final tracer sorption coefficient .13016E-04 m 

Percent recovery of tracer injected 99.552 % 

Accuracy index (0.0 = Perfect Recov.) .4481E-02 

Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).

98
Figure 19. Normalized tracer concentration data for the QTRACER.DAT sampling station

data file.

99
Figure 20. Normalized tracer load data for the QTRACER.DAT sampling station data file.

100
Figure 21. Standardized time-concentration data for the QTRACER.DAT sampling station

data file.

101
7.2. RCA.D EXAMPLE OUTPUT

In Section 4.1. on page 50 a tracer test conducted at the RCA del Caribe Superfund site

(Barceloneta, P.R.) was used as an example for analysis. RCA.D is the header file read by

QTRACER2 and references the sampling station data file, RCA.DAT (Table 11), that provides

all the relevant information necessary for QTRACER2 processing of the data obtained for

that sampling station.

7.2.1. RCA.DAT Tracer-Breakthrough Curve

Figure 22 depicts the basic tracer-breakthrough curve generated by QTRACER2 and

analyzed by QTRACER2. Note that discharge was measured each time a water sample

was collected.

7.2.2. RCA.DAT Chatwin Plot

Figure 23 depicts the data plot and straight-line fit of the Chatwin parameter for longitudinal

dispersion generated by QTRACER2 and analyzed by QTRACER2. Note that the equation

for the straight-line and the relevant statistics describing the straight-line fit were generated

by QTRACER2.

7.2.3. RCA.DAT Output File

Figure 24 depicts the final analytical output generated by QTRACER2. Besides observing

the analytical results, note the end of the output file, which depicts the complete results

of the analysis. QTRACER2 performs this function even though only a single sampling

station data file was analyzed. As such, the total results are the same as those listed in the

main part of the output file.

7.2.4. RCA.DAT Normalized Tracer Concentration

Figure 25 depicts the normalized tracer concentration data generated by QTRACER2

according to the method described by Mull et al. (1988). Note the concentration units

for the y axis.

7.2.5. RCA.DAT Normalized Tracer Load

Figure 26 depicts the normalized tracer load data generated by QTRACER2 according to

the method described by Mull et al. (1988). Note the concentration units for the y axis.

102
Figure 22. Tracer-breakthrough curve for the RCA.DAT sampling station data file.

103
Figure 23. Plot and straight-line fit of the Chatwin parameter for the RCA.DAT sampling

station data file.

104
******************************************************************** 

* * 

* Listing of output for: RCA.DAT * 

* * 

******************************************************************** 

Limits to integration for the data file: RCA.DAT 

Lower integration limit .00000 hrs 

Upper integration limit 24.000 hrs 

The quantity of tracer recovered1.7403 kg 

1740.3 g 

.17403E+07 mg 

.17403E+10 ug 

Distance from input to outflow point 33.528 m 

(110.00 ft) 

Uncorrected for sinuosity 

Time to leading edge (first arrival) 5.0000 hrs 

Time to peak tracer concentration 6.9999 hrs 

For a peak tracer concentration 380.00 ug/L 

Figure 24. Output file for the RCA.DAT sampling station data file.

105
The mean tracer transit time

.35853 d 

8.6048 hrs 

516.24 min 

Variance for mean tracer time.21200E-01 d^2 

12.211 hrs^2 

43961. min^2 

Standard deviation for tracer time.14560 d 

3.4945 hrs 

209.67 min 

The mean tracer velocity93.753 m/d 

3.9064 m/hr 

.11111E-02 m/s 

Standard deviation for tracer velocity29.204 m/d 

1.2168 m/hr 

.33801E-03 m/s 

Dispersion coefficient .31943E-03 m^2/s 

Longitudinal dispersivity .29437 m 

Peclet number113.90 

Advection > Diffusion 

Figure 24. Output file for the RCA.DAT sampling station data file (continued).

106
The maximum tracer velocity

160.94 m/d 

6.7057 m/hr 

.18627E-02 m/s 

Flow-channel volume estimate 11.726 m^3 

Flow-channel cross-sectional area .34974 m^2 

Flow-channel surface area 21237. m^2 

Tracer sorption coefficient (channel) .83208E-01 m 

Hydraulic head loss along channel .30391E-06 m 

Based on a friction factor .10076E-01 

Estimated Reynolds number 635.17 

Based on an estimated tube diameter .66731 m 

and an hydraulic conductivity .11971E+06 m/s 

Estimated Froude number .47862E-03 

Based on an estimated hydraulic depth .52411 m 

Figure 24. Output file for the RCA.DAT sampling station data file (continued).

107
Molecular mass transport parameters 

Shear velocity .21585E-03 m/s 

Estimated Schmidt number 1140.0 

Estimated Sherwood number 139.57 

Mass transfer coef. from wall to flow .20915E-06 m/s 

Molecular diffusion layer thickness 4.7813 mm 

Percent recovery of tracer injected .65922 % 

Accuracy index (0.0 = Perfect Recov.) .9934 

Figure 24. Output file for the RCA.DAT sampling station data file (continued).

108
******************************************************************** 

* * 

* Listing of output for: RCA.DAT * 

* * 

******************************************************************** 

Total quantity of tracer recovered1.7403 kg 

1740.3 g 

Total aquifer volume estimate 11.726 m^3 

Total aquifer surface area estimate 21237. m 

Final tracer sorption coefficient .83208E-01 m 

Percent recovery of tracer injected .65922 % 

Accuracy index (0.0 = Perfect Recov.) .9934 

Figure 24. Output file for the RCA.DAT sampling station data file (continued).

109
Figure 25. Normalized tracer concentration data for the RCA.DAT sampling station data file.

110
Figure 26. Normalized tracer load data for the RCA.DAT sampling station data file.

111
7.2.6. RCA.DAT Standardized Time-Concentration Data

Figure 27 depicts the standardized-time concentration data generated by QTRACER2

according to the method described by Mull et al. (1988). Note the time units on the x

axis and the concentration units on the y axis.

7.3. ANALYSIS ASSESSMENT OF THE QTRACER AND RCA EXAMPLE

DATA FILES

From the two examples (QTRACER and RCA), it is apparent that QTRACER2 is not

affected by variable discharges versus a constant discharge. QTRACER2 is also not affected

by recovery at a spring versus recovery at a monitoring well.

The QTRACER data set resulted in nearly perfect mass recovery. Had the QTRACER

data set been analyzed according to the description given in Section 4. on page 48, the user

would have noted a mass recovery > 100%. The efficient integration algorithms used by

QTRACER2 results in a more reliable mass balance.

QTRACER2 results for the RCA data set were quite similar to those presented in

Section 4.1.1. on page 51 QTRACER2 performs equally well on less ideal sites (e.g.,

TOPLITA).

7.3.1. Molecular Diffusion Layer Thickness

An estimate of the molecular diffusion layer thickness δm appears at the end of Figures 18

and 24. It is useful for understanding mass transfer from the walls of a karst conduit into

the main flow stream. Estimation of δm may be achieved from (Dreybrodt, 1988, p. 172)

Nsh = DC/δm (72)

where the Sherwood number Nsh for turbulent flow is obtained from (Dreybrodt, 1988, p.

172)

Nsh = 0.023N0.83N1/3

R (73) sc

which is valid for 0.6 ≤ Nsc ≤ 2500 and 2000 ≤ NR ≤ 35000. For laminar flow conditions

Nsh may be estimated from

0.668(DC/xs)NRNsc Nsh = 3.65 + 1+0.04[(DC/xs)NRNsc]

0.67 (74)

112
Figure 27. Standardized time-concentration data for the RCA.DAT sampling station data

file.

113
A mass transfer coefficient kf is obtained from the Sherwood number by using the

relationship (Dreybrodt, 1988, p. 171)

kfDC Nsh = (75) Dm

where the molecular diffusivity is on the order of 10−9 m2 s−1 (Neretnieks, 1993, p. 109).

The Schmidt number Nsc relates momentum and mass transfer. It is estimated by

relating the molecular diffusivity of the tracer to the kinematic viscosity of the water

according to the relationship

μ Nsc = (76) ρDm

It will be noted here that Dm = 1.0 × 10−9 (L2 T−1) is taken as a general value for

all tracer tests in QTRACER2 because it is too demanding that every possible tracer

diffusion coefficient be identified in QTRACER2. It is also assumed that the average user

of QTRACER2 will be unfamiliar with the appropriate value for Dm, making it impractical

to expect a user to provide an accurate value. For these reasons, any calculations using Dm

should be regarded as being only rough approximations.

114
8. QTRACER ANALYSIS OF OTHER HYDROLOGICAL SETTINGS

The previous version of QTRACER2 (QTRACER) was primarily designed for analysis of

BTCs from tracing tests conducted in karstic terranes (e.g., solution conduits) and fracturedrock terranes. The previous version noted that BTCs conducted in other hydrological

systems could be analyzed as well, but that much of the latter results may not be relevant

(e.g., Froude number for a porous-media tracer test) and the user had to know which

parameters to ignore. However, as explained in Section 6.6. on page 72 (see also Figure 15

on page 73) a new sampling station data file entry addressing the type of hydrological system

is provided for in QTRACER2.

8.1. SURFACE-WATER AND POROUS-MEDIA EXAMPLES

QTRACER2 now allows an entry for the type “FLOW MEDIUM” with an additional entry

for the “POROSITY”:

Subsurface Channel = 1 A subsurface channel is considered representative of any type

of karstic-solution conduit, mine shaft or tunnel, or any other type of submerged

conduit.

Surface Channel = 2 A surface channel is considered representative of any surface-water

flow from a very small creek to a large river.

Porous Medium = 3 Porous medium is exactly what it sounds like; any type of flow

through porous media. This can be a granular aquifer (e.g., alluvial aquifer) that

flows through a packed column in the laboratory. If porous-media flow is chosen, then

the user has the option of including a porosity value and a hydraulic conductivity

value.

Fractured Medium = 4 This last item addresses flow through a fractured-rock aquifer in

which a fracture porosity is important or flow through a single linear fracture (porosity

= 100%). If fracture flow is chosen, the user has the option of including an estimated

porosity value and an estimated fracture height value.

8.1.1. Surface-Water Example

A small stream, Uvas Creek, was traced in 1976 using a steady three hour injection of 1068 g

of Cl− in late summer during a low-flow period (Bencala and Walters, 1983; Zand, et al.,

115
1976). The emphasis of the tracing test was to investigate the mass-transport processes in

a small stream. The experimental study was limited to a 610 m reach with widths ranging

from 0.3 to 4 m. Flow rate at the time of the study was 45.0 m3 h−1. Time-concentration

measurements were taken at selected reaches where measured flow rates varied slightly from

45.0 m3 h−1. For this evaluation, tracer recovery at reach 281 m was used. The channel was

composed of a rough bed with alternating pools and riffles and a steep slope (0.03 m m−1).

This study included several sampling stations along the entire reach of the study. In this

particular case, individual runs for each sampling station should be run by QTRACER2

because summation function built into QTRACER2 would incorrectly sum the results for

the same tracer-recovery data.

Figure 28 and Figure 29 are the BTC and Chatwin plots of the UVAS Creek data set,

respectively. Figure 30 is the output file generated by QTRACER2 on the Uvas Creek data

set.

A cursory inspection of Figure 28 will show that plotting was initiated at some value

greater than zero. Background Cl

− concentrations at the site were taken as 3.71 mg L−1

and are included in the data file for plotting. The background concentration is subtracted

from the actual data file prior to any actual data analysis.

It will be noted that Figure 30 differs in some unique ways from Figures 18 and 24

(pages 94 and 105, respectively). For example, both Figures 18 and 24 provide an estimate

for the standard deviation for the mean tracer velocity, but no such listing is provided

in Figure 30. No standard deviation for mean tracer velocity could be estimated for the

UVAS281.DAT data set because the pulse-injection time exceeded the mean time of travel.

As indicated in Section 3.3.1. on page 32, this calculation is not trivial. More significant is

the fact that the upper limit to integration was necessarily changed from 29.867 hours to

4.3333 hrs (Figure 30) because tracer release was of a long-pulse type.

Transport-parameter estimates by QTRACER2 appears to be excellent. For example,

QTRACER2 estimated flow velocity to be 0.038 m s−1 which compares exceptionally well

with the published velocity of 0.037 m s−1 (Zand et al., 1976; Bencala and Walters, 1983)

obtained from Q/A. From Section 3.3.2. (page 36) it will be noted that in general, the

Chatwin method should provide a reasonable estimate for longitudinal dispersion even

though it is an incorrect method for pulse and continuous releases. Interestingly, by using

the Chatwin method, QTRACER2 estimated longitudinal dispersion to be 0.15 m s−1 which

compares favorably with the published longitudinal dispersion values of 0.24 m2 s−1 (Bencala

and Walters, 1983) and 0.25 m2 s−1 (Zand et al., 1976).

116
Figure 28. Tracer-breakthrough curve for the UVAS281.DAT sampling station data file.

117
Figure 29. Plot and straight-line fit of the Chatwin parameter for the UVAS281.DAT sampling

station data file.

118
******************************************************************** 

* * 

* Listing of output for: UVAS281.DAT * 

* * 

******************************************************************** 

Limits to integration for the data file: UVAS281.DAT 

Lower integration limit .00000 hrs 

Upper integration limit 29.867 hrs 

The quantity of tracer recovered1.3191 kg 

1391.1 g 

.13191E+07 mg 

.13191E+10 ug 

Distance from input to outflow point 281.00 m 

Uncorrected for sinuosity 

Time to leading edge (first arrival) .16667 hrs 

Time to peak tracer concentration 4.3333 hrs 

For a peak tracer concentration 6.2500 mg/L 

Figure 30. Output file for the UVAS281.DAT sampling station data file.

119
Upper Limit to integration necessarily changed! 

Lower integration limit 

Upper integration limit 

The mean tracer transit time 

Variance for mean tracer time 

Standard deviation for tracer time 

The mean tracer velocity 

Dispersion coefficient 

Longitudinal dispersivity 

Peclet number 

Figure 30. Output file for the UVAS281.DAT 

.00000 hrs

4.3333 hrs

.86625E-01 d

2.0790 hrs

124.74 min

.27233E-03 d^2

.15686 hrs^2

564.71 min^2

.16502E-01 d

.39606 hrs

23.764 min

3243.9 m/d

135.16 m/hr

.37545E-01 m/s

.15064 m^2/s

4.0122 m

70.037

Advection > Diffusion

sampling station data file (continued).

120
The maximum tracer velocity

40464. m/d 

1686.0 m/hr 

.46833 m/s 

Flow-channel volume estimate 104.78 m^3 

Flow-channel cross-sectional area .37289 m^2 

Flow-channel surface area .75270E+06 m^2 

Tracer sorption coefficient (channel) 0.0000 m 

Hydraulic head loss along channel .44516E-01 m 

Based on a friction factor 1.5189 

Viscous-flow sublayer along walls .80813 mm 

Estimated Reynolds number 22692. 

Based on an estimated tube diameter .68904 m 

Estimated Froude number .16297E-01 

Based on an estimated hydraulic depth .54117 m 

Figure 30. Output file for the UVAS281.DAT sampling station data file (continued).

121
Molecular mass transport parameters 

Shear velocity ..28996E-01 m/s 

Estimated Schmidt number 1140.0 

Estimated Sherwood number 991.01 

Mass transfer coef. from wall to flow .14383E-05 m/s 

Molecular diffusion layer thickness .69529 mm 

Percent recovery of tracer injected 123.51 % 

Accuracy index (0.0 = Perfect Recov.) -.2351 

******************************************************************* 

* * 

* AN IMPOSSIBLE CONDITION EXISTS! CHECK YOUR UNITS FOR * 

* CORRECTNESS OR CHECK TO SEE IF SAMPLE CONTAMINATION * 

* HAS OCCURRED (i.e., HAS SOMEONE ELSE BEEN INJECTING * 

* THE SAME TRACER MATERIAL IN THE AREA?). ALSO CHECK * 

* YOUR LIMITS TO INTEGRATION AND YOUR DISCHARGE ESTIMATES. * 

* DISCHARGE ESTIMATION ERRORS ARE VERY COMMON. TRACER * 

* RECOVERY SHOULD NOT BE GREATER THAN 100% AND THE * 

* ACCURACY INDEX SHOULD NOT BE LESS THAN ZERO. * 

* * 

******************************************************************* 

Figure 30. Output file for the UVAS281.DAT sampling station data file (continued).

122
******************************************************************** 

* * 

* Listing of output for: UVAS281.DAT * 

* * 

******************************************************************** 

Total quantity of tracer recovered1.3191 kg 

1391.1 g 

Total aquifer volume estimate 104.78 m^3 

Total aquifer surface area estimate .75270E+06 m 

Final tracer sorption coefficient 0.0000 m 

Percent recovery of tracer injected 123.51 % 

Accuracy index (0.0 = Perfect Recov.) -.2351 

******************************************************************* 

* * 

* AN IMPOSSIBLE CONDITION EXISTS! CHECK YOUR UNITS FOR * 

* CORRECTNESS OR CHECK TO SEE IF SAMPLE CONTAMINATION * 

* HAS OCCURRED (i.e., HAS SOMEONE ELSE BEEN INJECTING * 

* THE SAME TRACER MATERIAL IN THE AREA?). ALSO CHECK * 

* YOUR LIMITS TO INTEGRATION AND YOUR DISCHARGE ESTIMATES. * 

* DISCHARGE ESTIMATION ERRORS ARE VERY COMMON. TRACER * 

* RECOVERY SHOULD NOT BE GREATER THAN 100% AND THE * 

* ACCURACY INDEX SHOULD NOT BE LESS THAN ZERO. * 

* * 

******************************************************************* 

Figure 30. Output file for the UVAS281.DAT sampling station data file (continued).

123
Even more significant in Figure 30 is an error message that appears twice. This error

message indicates that more tracer mass was recovered than was injected. Although it

appears twice in Figure 30, it only appears in the case when > 100% tracer-mass is recovered.

In the case of Figure 30, excess tracer-mass recovery occurred at the single sampling station

that was considered. It is possible that individual sampling stations may result in < 100%,

but that their sum could result in > 100%.

8.1.2. Porous-Media Example

An injection-withdrawal two-well tracer test consists of injecting water containing tracer

into an injection well and withdrawing water from an extraction well at an equal rate so

that equilibrium may be established. Such a test was conducted in a soil borrow area at

the Barry Steam Plant of the Alabama Power company near Mobile, Alabama in the late

summer of 1984. The surface is composed of Quaternary age low-terrace deposits consisting

of interbedded sands and clays down to a depth of 61 m. Below these deposits a Miocene

series of undifferentiated sands, silty clays, and thin-bedded limestones extend to a depth

of 305 m (Molz, et al. 1986a, p. 38).

At the Mobile site, bromide was injected into a well over a period of 3.19 days. The

entire tracer test lasted 32.5 days (Molz, et al. 1986b). The injection and withdrawal

wells, separated by a distance of 38.3 m, were operated continuously at 57 m3 h−1 (Molz, et 

al. 1986a, p. 55) to cause steady-state conditions between the injection-withdrawal wells.

Details of the test are described in (Molz, et al. 1986a, p. 52–60, 71) and (Molz, et al. 

1986b).

Figure 31 and Figure 32 are the BTC and Chatwin plots of the UVAS Creek data set,

respectively. Figure 33 is the output file generated by QTRACER2 on the Uvas Creek data

set.

As with Figure 30, Figure 33 also differs in some unique ways from Figures 18 and 24

(pages 94 and 105, respectively). For example, both Figures 18 and 24 provide an estimate

for the surface area and sorption coefficient, but no such listing is provided in Figure 33. No

surface area or sorption coefficient could be estimated for the MOBILE.DAT data set because

the porous-media systems require some knowledge regarding particle diameter that is not

provided for in QTRACER2. In addition, a Froude number is not estimated because a

Froude number is not relevant to porous-media systems.

124
Figure 31. Tracer-breakthrough curve for the MOBILE.DAT sampling station data file.

125
Figure 32. Plot and straight-line fit of the Chatwin parameter for the MOBILE.DAT sampling

station data file.

126
******************************************************************** 

* * 

* Listing of output for: MOBILE.DAT * 

* * 

******************************************************************** 

Limits to integration for the data file: MOBILE.DAT 

Lower integration limit .00000 hrs 

Upper integration limit 760.00 hrs 

The quantity of tracer recovered362.29 kg 

.36229E+06 g 

.36229E+09 mg 

.36229E+12 ug 

Distance from input to outflow point 38.300 m 

Uncorrected for sinuosity 

Time to leading edge (first arrival) 9.8000 hrs 

Time to peak tracer concentration 209.00 hrs 

For a peak tracer concentration 22.000 mg/L 

Figure 33. Output file for the MOBILE.DAT sampling station data file.

127
The mean tracer transit time 

Variance for mean tracer time 

Standard deviation for tracer time 

The mean tracer velocity 

Standard deviation for tracer velocity 

Dispersion coefficient 

Longitudinal dispersivity 

Peclet number 

Figure 33. Output file for the MOBILE.DAT 

14.985 d

359.64 hrs

21579. min

50.094 d^2

28854. hrs^2

.10387E+09 min^2

7.0777 d

169.86 hrs

10192. min

2.9720 m/d

.12383 m/hr

.34398E-04 m/s

2.6669 m/d

.11112 m/hr

.30867E-04 m/s

.10476E-03 m^2/s

3.0456 m

12.576

Advection > Diffusion

sampling station data file (continued).

128
The maximum tracer velocity 

Transport-zone volume estimate 

Transport zone cross-sectional area 

Hydraulic head loss along channel 

Estimated Reynolds number 

Figure 33. Output file for the MOBILE.DAT 

129

9.3796 m/d 

.39082 m/hr 

.10856E-03 m/s 

20456. m^3 

534.11 m^2 

.26349E-04 m 

.72743E-01 

sampling station data file (continued).
Molecular mass transport parameters 

Estimated Schmidt number 1140.0 

Estimated Sherwood number 1.8708 

Percent recovery of tracer injected 46.388 % 

Accuracy index (0.0 = Perfect Recov.) 0.5361 

Figure 33. Output file for the MOBILE.DAT sampling station data file (continued).

130
******************************************************************** 

* * 

* Listing of output for: MOBILE.DAT * 

* * 

******************************************************************** 

Total quantity of tracer recovered362.29 kg 

.36229E+06 g 

Total aquifer volume estimate 20456. m^3 

Percent recovery of tracer injected 46.388 % 

Accuracy index (0.0 = Perfect Recov.) 0.5361 

Figure 33. Output file for the MOBILE.DAT sampling station data file (continued).

131
9. DATA INTERPOLATION AND EXTRAPOLATION EFFECTS

As explained in Section 5.1. on page 58, QTRACER2 uses a very efficient data interpolation

routine. The primary use of the data interpolation routine is when the user believes that

missing data points can be reasonably approximated by data interpolation. For example, if

the user believes that unaltered BTCs suggest that data aliasing may have occurred, then

data interpolation may be able to confirm or deny if aliasing has actually occurred.

9.1. COMPARISON OF QTRACER.DAT OUTPUT FILES

To illustrate the effect of data interpolation, data extrapolation, and the combined effect of

both on a data set exhibiting good mass recovery, the QTRACER.DAT data set was subjected

to each of these three algorithms. In some instances, the effect is fairly noticeable while in

other instances there are no differences.

9.1.1. Interpolated QTRACER.DAT BTC

Figure 34 depicts the interpolated BTC generated and analyzed by QTRACER2. Note that

discharge has an interpolated value for each time an interpolated tracer concentration value

was created.

9.1.2. Interpolated QTRACER.DAT Chatwin Plot

Figure 35 depicts the interpolated data plot and straight-line fit of the Chatwin parameter

for longitudinal dispersion generated and analyzed by QTRACER2. Note that the equation

for the straight-line and the relevant statistics describing the straight-line fit were generated

by QTRACER2.

Some difference will be noted between Figure 35 and Figure 17 (page 93), but not a

significant difference. Interpolation results in more data points falling on the necessary

straight line; the equation of the straight line has different values for the y intercept and

slope. As such, a slightly different estimate for longitudinal dispersion results.

Table 12 compares the final analytical output for the unaltered BTC for the QTRACER.DAT

data set, the interpolated QTRACER.DAT data set, and the Interpolated-extrapolated

QTRACER.DAT data set. Note how each file’s results are closely matched with the others.

132
Figure 34. Interpolated curve for the QTRACER.DAT sampling station data file.

133
Figure 35. Interpolated data set for the Chatwin parameter for the QTRACER.DAT sampling

station data file.

134
Table 12. Estimated hydraulic flow and geometric parameters from BTCs for QTRACER.DAT samp

Parameter QTRACER.DAT QTRACER.DAT QTRACER.DAT1 QTRA

(unaltered) (interpolated) (extrapolated) (inter

135

Tracer Mass

Recovered, g

Percent Mass

Recovered

Accuracy

Index

Initial Tracer

Breakthrough, h

Time to Peak

Concentration, h

Mean Tracer

Residence Time, h

Elapsed Tracer

Travel Time, h

Maximum Tracer

Flow Velocity, m h−1

Peak Tracer

Flow Velocity, m h−1

Mean Tracer

Flow Velocity, m h−1

Shear

Velocity, m h−1

Longitudinal

Dispersion, m2 h−1

Hydraulic

Head Loss, m

4.48 × 102 4.48 × 102 4.48 × 102 4.48 

9.96 × 101 9.95 × 101 9.96 × 101 9.96 

4.48 × 10−3 4.75 × 10−3 3.67 × 10−3 3.80 

7.00 × 100 6.20 × 100 7.00 × 100 6.10 

8.00 × 100 8.00 × 100 8.00 × 100 8.00 

9.27 × 100 9.26 × 100 9.28 × 100 9.27 

2.00 × 101 2.00 × 101 2.26 × 101 2.32 

3.86 × 102 4.36 × 102 3.86 × 102 4.43 

3.38 × 102 3.38 × 102 3.38 × 102 3.38 

2.91 × 102 2.92 × 102 2.91 × 102 2.91 

6.12 × 101 6.13 × 101 6.12 × 101 6.12 

1.17 × 104 8.57 × 103 1.17 × 104 7.68 

1.21 × 10−2 1.21 × 10−2 1.21 × 10−2 1.21 

continued 
sa

continued 

QTRA

(inter

1.10 1.13 1.38 1.01 1.50 5.54 5.17 8.40 6.59 5.96 1.02 1.14 

Estimated hydraulic flow and geometric parameters from BTCs for QTRACER.DAT

QTRACER.DAT1

(extrapolated)

1.07 × 10−51.13 × 10−11.38 × 10−31.01 × 10−21.50 × 1035.54 × 1015.16 × 1078.40 × 1006.60 × 1005.95 × 1056.70 × 1011.14 × 103

QTRACER.DAT

(interpolated)

1.38 × 10−51.13 × 10−11.38 × 10−31.01 × 10−21.49 × 1055.53 × 1015.17 × 1078.39 × 1006.59 × 1005.96 × 1059.19 × 1011.14 × 103

QTRACER.DAT

1.30 × 10−5

1.13 × 10−1

1.38 × 10−3

1.01 × 10−2

(unaltered)

1.49 × 105

5.53 × 101

5.17 × 107

8.39 × 100

6.59 × 100

5.96 × 105

6.70 × 101

1.14 × 103

Sectional Area, m2

Flow-Channel CrossSurface Area, m2

Coefficient, mDiameter, m

Tracer Sorption

Sublayer, mVolume, m3

Flow-ChannelFlow-Channel

Viscous-Flow

Depth, mNumberNumberNumberNumber

Parameter

Factor

HydraulicReynoldsSchmidtFriction

(continued). 

FroudeP ́ecletTube

Table 12.

136
sa

QTRA

(inter

1.78 5.63 1.49 

Estimated hydraulic flow and geometric parameters from BTCs for QTRACER.DAT

QTRACER.DAT1

(extrapolated)

1.78 × 10−65.63 × 10−41.49 × 104

QTRACER.DAT

(interpolated)

1.78 × 10−65.62 × 10−41.49 × 104

layer, m

Listed parameters without dimensions are dimensionless.

1Extrapolated using a statistical straight line fit.2Extrapolated using a cubic Hermite function.

QTRACER.DAT

1.78 × 10−6

5.62 × 10−4

(unaltered)

1.49 × 104

Coefficient, m s−1

Molecular diffusion

Mass Transfer

Number

ParameterSherwood

(continued). Table 12.

137
9.1.3. Extrapolated QTRACER.DAT BTC

Figure 36 depicts the extrapolated BTC generated and analyzed by QTRACER2. Note

that discharge has an interpolated value for each time an extrapolated tracer concentration

value is created.

Graphically, the user will note that the BTC shown in Figure 36 appears relatively

unchanged from Figure 16. The only apparent difference is that the elapsed tracer travel

time has been extended from 20 hours to > 22 hours and that one additional data point

(total data = 22) has been included.

More obvious is the effect of data extrapolation on the discharge curve when data

extrapolation routines 1 (exponential decay) and 3 (statistical fit) are employed (3 =

statistical fit for Figure 36). Extrapolation routine 2 (piecewise cubic Hermite) uses the

shape of the entire existing data curve to determine the “most reasonable” extrapolation

data point possible for the extrapolated discharge.

Extrapolation routines 1 and 3, however, have no mathematical basis for consideration.

For example, there is no reason to assume that discharge will behave as an exponential

decay function, so extrapolation routine 1 = exponential decay would make no physical

sense. Therefore, when extrapolation routines 1 or 3 are requested and a variable discharge

is measured, QTRACER2 will automatically extend the discharge curve in the opposite

vertical direction (along the y axis) to one-half its previous range. It is up to the user to

decide on its reasonableness.

9.1.4. Extrapolated QTRACER.DAT Chatwin Plot

Figure 37 depicts the extrapolated data plot and straight-line fit of the Chatwin parameter

for longitudinal dispersion generated and analyzed by QTRACER2. Note that the straightline fit, the equation for the straight line, and the relevant statistics describing the straightline fit generated by QTRACER2 are identical to Figure 17. Data extrapolation had no

effect on the Chatwin method analysis because the original sample had resulted in nearly

“complete” tracer recovery.

9.2. INTERPOLATED-EXTRAPOLATED QTRACER.DAT DATA

Figures 38 and 39 illustrate how the interpolation and extrapolation routines provided in

QTRACER2 can be used in BTC analyses. Table 12 illustrates that there are no significant

differences in any of the analyses provided by QTRACER2 for the QTRACER.DAT data set.

138
Figure 36. Extrapolated curve for the QTRACER.DAT sampling station data file.

139
Figure 37. Extrapolated data set for the Chatwin parameter for the QTRACER.DAT sampling

station data file.

140
Figure 38. Interpolated and extrapolated data set for the QTRACER.DAT sampling station

data file.

141
Figure 39. Interpolated and extrapolated data for the Chatwin parameter for QTRACER.DAT 

sampling station data file.

142
A more erratic BTC, or one that was ended leaving a significant mass of tracer in the

system, would result in large differences when data interpolation and/or extrapolation is

employed. The user should note that when data extrapolation are employed without data

interpolation, the graphics may appear incorrect (i.e., a straight-line connection from the

last measured data point to the extrapolated data point). This apparent inaccuracy is not

a problem, however, as it is strictly an artifact of the plotting algorithm. The integration

routine used by QTRACER2 will develop a smooth curve between all provided data points

regardless of BTC appearance.

9.3. COMPARISON OF RCA.DAT OUTPUT FILES

To further illustrate the effect of data interpolation, data extrapolation, and the combined

effects of both on a data set exhibiting poor mass recovery, the RCA.DAT data set was

subjected to each of these three algorithms. In some instances, the effect is fairly noticeable,

while in other instances there are no differences.

9.3.1. Interpolated RCA.DAT BTC

Figure 40 depicts the interpolated BTC generated and analyzed by QTRACER2. Note that

discharge has no interpolated value. This is because discharge was considered a constant,

so there are no data to interpolate.

Graphically, the user will note that Figure 40 is little changed from the curve shown in

Figure 22. The slight improvement is most evident at the peak, where the interpolated file

more correctly matches the peak concentration data point. In Figure 22, the graphics line

slightly exceeds the time to peak concentration. However, the apparent inaccurate plotting

is NOT reflected in the actual data analysis by QTRACER2.

9.3.2. Interpolated RCA.DAT Chatwin Plot

Figure 41 depicts the interpolated data plot and straight-line fit of the Chatwin parameter

for longitudinal dispersion generated and analyzed by QTRACER2. Note that the equation

for the straight-line and the relevant statistics describing the straight-line fit were generated

by QTRACER2.

Some difference will be noted between Figure 41 and Figure 23, but not a greatly

significant difference. Interpolation results in more data points falling on the necessary

straight line, and the equation of the straight line has different values for the y intercept

and slope. As such, a slightly different estimate for longitudinal dispersion will result.

143
Figure 40. Interpolated curve for the RCA.DAT sampling station data file.

144
Figure 41. Interpolated data set for the Chatwin parameter for the RCA.DAT sampling

station data file.

145
Table 13. Estimated hydraulic flow and geometric parameters from BTCs for RCA.DAT 

sampling station.

Parameter RCA.DAT RCA.DAT RCA.DAT1 RCA.DAT2

(unaltered) (interpolated) (extrapolated) (inter./extra.)

Tracer Mass 1.74 × 103 1.74 × 103 1.77 × 103 1.77 × 103

Recovered, g

Percent Mass 6.59 × 10−1 6.59 × 10−1 6.70 × 10−1 6.71 × 101

Recovered

Accuracy 9.93 × 10−1 9.93 × 10−1 9.93 × 10−1 9.93 × 10−1

Index

Initial Tracer 5.00 × 100 4.08 × 100 5.00 × 100 4.08 × 100

Breakthrough, h

Time to Peak 7.00 × 100 6.96 × 100 7.00 × 100 6.96 × 100

Concentration, h

Mean Tracer 8.61 × 100 8.60 × 100 8.90 × 100 8.95 × 100

Residence Time, h

Elapsed Tracer 2.40 × 101 2.40 × 101 3.17 × 101 5.20 × 101

Travel Time, h

Maximum Tracer 6.71 × 100 8.22 × 100 6.71 × 100 8.22 × 100

Flow Velocity, m h−1

Peak Tracer 4.79 × 100 4.82 × 100 4.79 × 100 4.82 × 100

Flow Velocity, m h−1

Mean Tracer 3.91 × 100 3.91 × 100 3.78 × 100 3.76 × 100

Flow Velocity, m h−1

Shear 7.77 × 10−1 7.77 × 10−1 7.58 × 10−1 7.55 × 10−1

Velocity, m h−1

Longitudinal 1.15 × 100 1.29 × 100 1.15 × 100 1.38 × 100

Dispersion, m2 s−1

Hydraulic 3.04 × 10−7 3.04 × 10−7 2.85 × 10−7 2.81 × 10−7

Head Loss, m

Flow-Channel 1.17 × 101 1.17 × 101 1.21 × 101 1.22 × 101

Volume, m3

Flow-Channel Cross- 3.50 × 10−1 3.50 × 10−1 3.62 × 10−1 3.64 × 10−1

Sectional Area, m2

Flow-Channel 2.12 × 104 2.12 × 104 2.11 × 104 2.10 × 104

Surface Area, m2

Tracer Sorption 8.32 × 10−2 8.32 × 10−2 8.53 × 10−2 8.57 × 10−2

Coefficient, m

Tube 6.67 × 10−1 6.67 × 10−1 6.79 × 10−1 6.80 × 10−1

Diameter, m

continued on next page 

146
Table 13. Estimated hydraulic flow and geometric parameters from BTCs for RCA.DAT 

sampling station (continued). 

Parameter RCA.DAT RCA.DAT RCA.DAT1 RCA.DAT2

(unaltered) (interpolated) (extrapolated) (inter./extra.)

Friction 1.01 × 10−1 1.01 × 10−1 1.02 × 10−1 1.03 × 10−1

Factor

Laminar Hydraulic 1.20 × 105 1.20 × 105 1.24 × 105 1.25 × 105

Conductivity, m s−1

Reynolds 6.35 × 102 6.35 × 102 6.25 × 102 6.23 × 102

Number

Froude 4.79 × 10−4 4.79 × 10−4 4.59 × 10−4 4.56 × 10−4

Number

P ́eclet 1.14 × 102 1.02 × 102 1.10 × 102 9.16 × 101

Number

Schmidt 1.14 × 103 1.14 × 103 1.14 × 103 1.14 × 103

Number

Sherwood 1.40 × 102 1.40 × 102 1.40 × 102 1.40 × 102

Number

Mass Transfer 2.09 × 10−7 2.09 × 10−7 2.06 × 10−7 2.05 × 10−2

Coefficient, m s−1

Molecular diffusion 4.78 × 10−3 4.78 × 10−3 4.86 × 10−3 4.87 × 10−3

layer, m

Listed parameters without dimensions are dimensionless.

1Extrapolated using a statistical straight line fit.

2Extrapolated using a cubic Hermite function.

Table 13 compares the final analytical output for the unaltered BTC for the RCA.DAT 

data set, the interpolated RCA.DAT data set, and the interpolated-extrapolated RCA.DAT 

data set. Note how each file’s results are closely matched with the others.

9.3.3. Extrapolated RCA.DAT BTC

Figure 42 depicts the extrapolated BTC generated and analyzed by QTRACER2. Note

that discharge has no extrapolated value because discharge was constant.

Graphically, the user will note that Figure 42 is more reasonable than Figure 22. The

improvement is most evident in the elapsed time of travel. In Figure 22, the elapsed time of

travel (24 hours) is reflected in a cessation of sample collection prior to “complete” tracer

recovery. However, Figure 42 suggests nearly “complete” tracer recovery at > 30 hours.

147
Figure 42. Extrapolated curve for the RCA.DAT sampling station data file.

148
9.3.4. Extrapolated RCA.DAT Chatwin Plot

Figure 43 depicts the extrapolated data plot and straight-line fit of the Chatwin parameter

for longitudinal dispersion generated and analyzed by QTRACER2. Note that the straightline fit, equation for the straight-line, and relevant statistics describing the straight-line fit

generated by QTRACER2 are slightly different from the results shown in Figure 23.

The obvious differences between Figure 43 and Figure 23 are a result of not having

continued actual data collection until near “complete” tracer recovery. Because sampling

ceased before adequate tracer recovery, data extrapolation exerts considerable influence on

the Chatwin analysis; in this instance, a straight-line fit to the data that is not as good.

9.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA

Figures 44 and 45 illustrate how the interpolation and extrapolation routines provided in

QTRACER2 can be used in BTC analyses. Table 13 illustrates that there are no significant

differences in any of the analyses provided by QTRACER2 for the RCA.DAT data set.

The user will note in Figure 44 that the exponential decay equation

−0.215973x y = 660.115 e (77)

has been produced along with the correlation coefficient r (-0.9418) and the standard error

of the estimated fit (50.87). QTRACER2 provides this information to the user to assist in

assessing the effect of an exponential decay on a BTC. Whereas extrapolation methods 2 

(piecewise cubic Hermite) and 3 (statistical method) produce a single extrapolated point,

method 1 (exponential decay) produces five additional data points and thus has a great deal

more influence on the final results.

Exponential decay extrapolation has more influence because the integration routine

employed by QTRACER2 is forced to conform to the shape of the exponentially decaying

curve. It is therefore incumbent upon the user to determine how appropriate it is to use

an exponential decay model for extrapolation. For example, applying an exponential decay

model for extrapolation to the QTRACER.DAT data set results in tracer mass recovery that

is greater than what was injected. Clearly this is an impossibility that suggests major field

errors, laboratory errors, numerical errors, or some combination of all three.

A more erratic BTC or one that was ended leaving a significant mass of tracer in the

system would result in large differences when data interpolation and/or extrapolation are

employed. The user should note that when data extrapolation is employed without data

149
Figure 43. Extrapolated data set for the Chatwin parameter for the RCA.DAT sampling

station data file.

150
Figure 44. Interpolated and extrapolated data set for the RCA.DAT sampling station data

file.

151
Figure 45. Interpolated and extrapolated data for the Chatwin parameter for RCA.DAT 

sampling station data file.

152
interpolation, the graphics may appear incorrect (i.e., a straight-line connection from the

last measured data point to the extrapolated data point). This apparent inaccuracy is not

a problem, however, as it is strictly an artifact of the plotting algorithm. The integration

routine used by QTRACER2 will develop a smooth curve between all provided data points

regardless of BTC appearance.

153
10. ASSOCIATED COMPUTER PROGRAMS

To facilitate the efficient use of QTRACER2, three additional programs have been developed

and included with this package. The first, NDATA, allows the user to run an efficient

interpolation program to fill missing data in either the time-concentration or the timedischarge data files. The second program, AUTOTIME, converts time-concentration data

files using military time into sequential decimal time as required by QTRACER2. The

third program, DATFILE, provides a straightforward interface for the creation of a sample

station data file.

The results of these three programs are easily appended or copied to a *.DAT file (see

Section 6.6.24. on page 88 and the end of Figure 15). By judicious use of these programs,

QTRACER2 can be made more efficient because the data can be quickly and easily placed

inrequi red form.

10.1. NDATA COMPUTER PROGRAM

Typically, discharge is not measured as frequently or at the same time as tracer concentration. Hence, the time concentration data file might appear as (no specific data file example):

0.0 0.00 4.10 

1.0 2.05 

5.0 4.50 3.96 

10.0 4.10 

15.0 4.33 

20.0 0.03 3.80 

The data file cannot be processed because values for discharge and corresponding values

for concentration must also be recorded in the file (unless a constant discharge was listed

above). To resolve this problem, NDATA.EXE, a very good data interpolation algorithm

has been programmed (it is the same one used in QTRACER2). To use this program, Left 

Double-Click on NDATA and follow the instructions. Note that this program ONLY works on

a time-concentration file or time-discharge file without any other headers. The algorithm

must therefore be used on the original data set(s) and the results copied to the bottom of

the final data file to be processed.

When using NDATA only X/Y data is recognized by the program as a data file. So if

you were missing some discharge values, create a set of X/Y values in which time values

correspond to X and discharge values correspond with Y. Do not use the concentration

values. The program can then be used to fill in missing discharge values. When typing in

154
the data, OMIT all time values for which a corresponding discharge or concentration value

is missing. Using the example above, if the concentration value corresponds to time=15.0,

the user would exclude the entire line from the data set to be processed. The greater the

number of missing data pairs, the greater the interpolation errors.

Note that NDATA is to be used to fill data gaps in both concentration data and discharge,

but only where corresponding values are missing. It is better to allow QTRACER2 to

perform data interpolation on a complete data file.

10.1.1. NDATA Source

The FORTRAN source code is included on the NDATA disk. Modification of the NDATA

main file can be relatively easily accomplished if desired, but is not recommended. The user

should not attempt to modify the included subroutines.

10.2. AUTOTIME COMPUTER PROGRAM

Tracer-breakthrough curve data is often recorded in military time as opposed to sequentially

from 0 to infinity. AUTOTIME will convert data recorded in military time into sequentially

listed time in terms of decimal seconds, decimal minutes, decimal hours, or decimal days

depending on the user’s preference.

The user must first create a time-concentration file such as that shown in Figure 46.

Left Double-Click AUTOTIME and then follow the instructions to create a new file of

time-concentration data that can then be copied to the end of a *.DAT file and read

by QTRACER2. Note that the concentration and discharge values are not altered by

AUTOTIME. Also note that a variable discharge recorded by the user is allowed in a third

column that is read by AUTOTIME. The third column is not necessary, however.

Running AUTOTIME on the data listed in Figure 46 for conversion to decimal hours

will result the file listed in Figure 47. As stated previously, that QTRACER2 allows for freeformat data entry, so a nicely formatted data column is unnecessary. All that is necessary

is that the two data columns be separated by at least one blank space or a comma.

10.2.1. AUTOTIME Source

The FORTRAN source code is included on the AUTOTIME disk. Modification of

the AUTOTIME main file can be relatively easily accomplished if desired, but is not

recommended.

155
10 15 0.010 3.23E-2 

21 45 0.010 3.23E-2 

22 15 0.060 3.23E-2 

22 45 0.500 3.23E-2 

23 15 1.320 3.23E-2 

23 45 2.050 3.23E-2 

0 15 3.900 3.23E-2 

0 45 4.200 3.23E-2 

1 15 4.200 3.23E-2 

1 45 3.400 3.23E-2 

2 15 3.050 3.23E-2 

2 45 2.450 3.23E-2 

3 15 2.000 3.23E-2 

3 45 1.500 3.23E-2 

4 15 1.200 3.23E-2 

4 45 0.950 3.23E-2 

5 15 0.800 3.23E-2 

5 45 0.600 3.23E-2 

6 15 0.550 3.23E-2 

6 45 0.500 3.23E-2 

7 15 0.420 3.23E-2 

7 45 0.370 3.23E-2 

8 15 0.350 3.23E-2 

8 45 0.300 3.23E-2 

13 45 0.200 3.23E-2 

22 45 0.010 3.23E-2 

Figure 46. Example of a sample time-concentration file using military time for conversion

(Mull et al., 1988).

156
0.0000 0.0100 0.0323

11.5000 0.0100 0.0323

12.0000 0.0600 0.0323

12.5000 0.5000 0.0323

13.0000 1.3200 0.0323

13.5000 2.0500 0.0323

14.0000 3.9000 0.0323

14.5000 4.2000 0.0323

15.0000 4.2000 0.0323

15.5000 3.4000 0.0323

16.0000 3.0500 0.0323

16.5000 2.4500 0.0323

17.0000 2.0000 0.0323

17.5000 1.5000 0.0323

18.0000 1.2000 0.0323

18.5000 0.9500 0.0323

19.0000 0.8000 0.0323

19.5000 0.6000 0.0323

20.0000 0.5500 0.0323

20.5000 0.5000 0.0323

21.0000 0.4200 0.0323

21.5000 0.3700 0.0323

22.0000 0.3500 0.0323

22.5000 0.3000 0.0323

27.5000 0.2000 0.0323

36.5000 0.0100 0.0323

Figure 47. Example of a converted sample time-concentration file created by AUTOTIME

(Mull et al., 1988).

157
10.3. DATFILE COMPUTER PROGRAM

The easiest method for creating a sample station data file (Figure 15) may be accomplished

by using a text editor to edit an existing sample station data file and saving the altered file

using a new filename. However, if desired, the user may use DATFILE to create a sample

station data file. In addition, DATFILE may be used to read in a QTRACER file (either a

*.D file or a *.DAT file) for quick conversion to a QTRACER2-readable file

To use DATFILE, the user need only Left Double-Click DATFILE and respond to each

requestor in turn. In the create mode, DATFILE only produces the upper portion of

a sampling station data file. The actual TIME CONCENTRATION DISCHARGE data

must be appended to the end of the data file created by DATFILE. In the conversion mode,

DATFILE attempts to automatically identify the type of file to be converted by recognizing

the first word of the file (QUANTITY = *.D file; SAMPLING = *.Dat file). If DATFILE

cannot identify the file, the user is requested to provide identification for DATFILE. Upon

recognition, the user then responds to a few appropriate requestors.

A sample station data file created or converted from a QTRACER-file form using

DATFILE will not appear exactly in the form of Figure 15 because of some formatting

differences. This is not a concern because QTRACER2 uses free format for input.

10.3.1. DATFILE Source

The FORTRAN source code is included on the DATFILE disk. Modification of the

DATFILE main file can be relatively easily accomplished if desired, but is not recommended.

10.4. COMBINE COMPUTER PROGRAM

Typically, as mentioned in Section 10.1. on page 154 discharge is not measured as frequently

or at the same time as tracer concentration. With the advent of continuous-flow filter

fluorometers, pressure transducers, and data loggers, automatic data recording is now

normally conducted. However, if the time settings on these various instruments are not

synchronized or one automatic recording device takes readings less frequently than the a

different recording device, then use of QTRACER in which one “universal” set of TIME

data is used is problematic. For example, consider the following time-concentration data set

(Combine1.dat; modified from the QTRACER.DAT file using the interpolation function of

QTRACER) shown in Figure 48 and the time-discharge data set (Combine2.dat; unmodifed

from the QTRACER.DAT file) shown in Figure 49.

158
0.000000000 0.000000000 

0.2000000030 0.000000000 

0.4000000060 0.000000000 

0.6000000238 0.000000000 

0.8000000119 0.000000000 

1.000000000 0.000000000 

1.200000048 0.000000000 

1.399999976 0.000000000 

1.600000024 0.000000000 

1.799999952 0.000000000 

2.000000000 0.000000000 

2.200000048 0.000000000 

2.400000095 0.000000000 

2.599999905 0.000000000 

2.799999952 0.000000000 

3.000000000 0.000000000 

3.200000048 0.000000000 

3.399999857 0.000000000 

3.599999905 0.000000000 

3.799999952 0.000000000 

4.000000000 0.000000000 

4.199999809 0.000000000 

4.399999619 0.000000000 

4.599999905 0.000000000 

4.799999714 0.000000000 

5.000000000 0.000000000 

5.199999809 0.000000000 

5.399999619 0.000000000 

5.599999905 0.000000000 

5.799999714 0.000000000 

6.000000000 0.000000000 

6.199999809 0.6205322146 

6.400000095 2.121600866 

6.599999905 3.962399006 

6.799999714 5.602131367 

7.000000000 6.500000000 

7.199999809 6.825866222 

7.400000095 7.101600170 

7.599999905 7.314399719 

7.800000191 7.451466560 

Figure 48. Example of a measured sample time-concentration file as recorded by an

automatic data recorded (modified from the QTRACER.DAT).

159
8.000000000 7.500000000 

8.199999809 7.284326077 

8.399999619 6.736979008 

8.599999428 6.007468700 

8.799999237 5.245306492 

9.000000000 4.599999905 

9.199999809 4.042011261 

9.399999619 3.470477104 

9.599999428 2.927937984 

9.799999237 2.456932783 

9.999999046 2.100001335 

10.19999886 1.822443485 

10.39999962 1.570183516 

10.59999943 1.356703877 

10.79999924 1.195482850 

10.99999905 1.100000262 

11.19999886 1.047596455 

11.39999866 1.005732298 

11.59999847 0.9730700850 

11.79999924 0.9482718706 

11.99999905 0.9300000668 

12.19999886 0.9165091515 

12.39999866 0.9060727954 

12.59999847 0.8973819017 

12.79999828 0.8891273141 

12.99999809 0.8800001144 

13.19999886 0.8703692555 

13.39999866 0.8611077666 

13.59999847 0.8516616225 

13.79999828 0.8414769769 

13.99999809 0.8300001025 

14.19999790 0.8168752193 

14.39999771 0.8021946549 

14.59999847 0.7860764265 

14.79999828 0.7686389089 

14.99999809 0.7500001788 

15.19999790 0.7302790880 

15.39999771 0.7090768218 

15.59999752 0.6857351661 

15.79999733 0.6595957875 

Figure 48. Example of a measured sample time-concentration file as recorded by an

automatic data recorded (modified from the QTRACER.DAT) (continued).

160
15.99999809 0.6300002933 

16.19999695 0.5930896401 

16.39999771 0.5479190350 

16.59999847 0.4982038140 

16.79999733 0.4476595819 

16.99999809 0.4000004232 

17.19999695 0.3527349830 

17.39999771 0.3033765852 

17.59999657 0.2556514442 

17.79999733 0.2132840753 

17.99999809 0.1800002754 

18.19999695 0.1541337073 

18.39999771 0.1314002424 

18.59999657 0.1116003171 

18.79999733 0.9453354031E-01 

18.99999619 0.8000025153E-01 

19.19999695 0.6706685573E-01 

19.39999771 0.5520012602E-01 

19.59999657 0.4480016232E-01 

20.00000000 0.2999999933E-01 

Figure 48. Example of a measured sample time-concentration file as recorded by an

automatic data recorded (modified from the QTRACER.DAT) (continued).

161
0.0 4.10 

1.0 4.20 

2.0 4.27 

3.0 4.35 

4.0 4.42 

5.0 4.50 

6.0 4.57 

7.0 4.67 

8.0 4.75 

9.0 4.82 

10.0 4.90 

11.0 4.80 

12.0 4.68 

13.0 4.56 

14.0 4.46 

15.0 4.33 

16.0 4.22 

17.0 4.12 

18.0 4.00 

19.0 3.90 

20.0 3.80 

Figure 49. Example of a measured sample time-discharge file as recorded by an automatic

data recorded (unmodified from the QTRACER.DAT).

162
The two data files do not correspond because, assuming these appear as recorded by

automatic recording devices, there are only 21 time-discharge data values, while there are

100 time-concentration data values. In this instance, each of the time values for the timedischarge data set has a matching time value in the time-concentration data set. However,

even if there were no matching time values between the two disparate data sets, COMBINE

would do a tolerable job of making a match.

To use COMBINE, the user need only start the program (Left Double-Click on the

COMBINE icon) and select units for time, concentration, and discharge which can be

arbitrary and are not necessary for the program to run. Next the user enters the timeconcentration data file to be considered, then the time-discharge data file to be considered,

then an output name for the resulting time-concentration-discharge data file, and a plot

file name if a PostScript file of the screen plot is desired. A screen plot of the resulting

time-concentration-discharge data file will be displayed if the chosen interpolation step is

not too small. A selected interpolation step of 0.1 is recommended as an initial value, but

the user is free to pretty much choose any value. However, a very small interpolation step

(e.g., 0.0001) will result in a massively huge file that may exceed the memory stack on the

local computer.

Processing the two data files shown above, Combine1.dat and Combine2.dat, using

COMBINE results in the following time-concentration-discharge data file shown in Figure 50.

10.4.1. COMBINE Screen Plotting

If the size of the created time-concentration-discharge file is of a reasonable size, COMBINE

will display a screen plot from which a bitmapped file may be created. A screen plot was

added so that the user may examine the results of the COMBINE-created file in relation

to the original time-concentration and time-discharge data files. Although only a visual

inpection, the screen plot allows the user the ability to verify that the COMBINE-created

file is acceptable.

Figure 51 (page 169) depicts the results of Figure 50. The open circles in Figure 51

represent measured time-concentration data points from Figure 48 and the open triangles

in Figure 51 represent measured time-discharge data points from Figure 49. The solid line

in Figure 51 represents the interpolated time-concentration data shown in Figure 50 and the

dashed line in Figure 51 represents the interpolated time-discharge data shown in Figure 50.

Although it is not readily apparent from Figure 51, the data listed in Figure 50 results

163
TIME CONCENTRATION DISCHARGE

0.0000000E+00 0.0000000E+00 

0.2000000 0.0000000E+00 

0.3000000 0.0000000E+00 

0.4000000 0.0000000E+00 

0.5000000 0.0000000E+00 

0.6000000 0.0000000E+00 

0.7000000 0.0000000E+00 

0.8000000 0.0000000E+00 

1.100000 0.0000000E+00 

1.200000 0.0000000E+00 

1.300000 0.0000000E+00 

1.400000 0.0000000E+00 

1.500000 0.0000000E+00 

1.600000 0.0000000E+00 

1.700000 0.0000000E+00 

1.800000 0.0000000E+00 

1.900000 0.0000000E+00 

2.000000 0.0000000E+00 

2.100000 0.0000000E+00 

2.200000 0.0000000E+00 

2.300000 0.0000000E+00 

2.400000 0.0000000E+00 

2.500000 0.0000000E+00 

2.600000 0.0000000E+00 

2.700000 0.0000000E+00 

2.800000 0.0000000E+00 

2.900000 0.0000000E+00 

3.000000 0.0000000E+00 

3.100000 0.0000000E+00 

3.200000 0.0000000E+00 

3.300000 0.0000000E+00 

3.400000 0.0000000E+00 

3.500000 0.0000000E+00 

3.600000 0.0000000E+00 

3.700000 0.0000000E+00 

3.800000 0.0000000E+00 

3.900000 0.0000000E+00 

4.100000 

4.122500 

4.133300 

4.143900 

4.154100 

4.164000 

4.173500 

4.182700 

4.208000 

4.215400 

4.222500 

4.229300 

4.236000 

4.242500 

4.249100 

4.255800 

4.262700 

4.270000 

4.277600 

4.285500 

4.293600 

4.301700 

4.310000 

4.318300 

4.326400 

4.334500 

4.342400 

4.350000 

4.357300 

4.364400 

4.371400 

4.378200 

4.385000 

4.391800 

4.398600 

4.405600 

4.412700 

Figure 50. Example of a converted sample time-concentration-discharge file created by

COMBINE for use in QTRACER.

164
4.000000 0.0000000E+00 

4.100000 0.0000000E+00 

4.200000 0.0000000E+00 

4.300000 0.0000000E+00 

4.400000 0.0000000E+00 

4.500000 0.0000000E+00 

4.600000 0.0000000E+00 

4.700000 0.0000000E+00 

4.800000 0.0000000E+00 

4.900000 0.0000000E+00 

5.000000 0.0000000E+00 

5.100000 0.0000000E+00 

5.200000 0.0000000E+00 

5.300000 0.0000000E+00 

5.400000 0.0000000E+00 

5.500000 0.0000000E+00 

5.600000 0.0000000E+00 

5.700000 0.0000000E+00 

5.800000 0.0000000E+00 

5.900000 0.0000000E+00 

6.000000 0.0000000E+00 

6.100000 0.2003800 

6.200000 0.6203800 

6.300000 1.273800 

6.400000 2.121300 

6.500000 3.031500 

6.600000 3.962100 

6.700000 4.853700 

6.800000 5.601900 

6.900000 6.136200 

7.000000 6.499900 

7.100000 6.685300 

7.200000 6.825800 

7.300000 6.971000 

7.400000 7.101500 

7.500000 7.217100 

7.600000 7.314400 

7.700000 7.394800 

4.420000 

4.427600 

4.435500 

4.443600 

4.451700 

4.460000 

4.468300 

4.476400 

4.484500 

4.492400 

4.500000 

4.507300 

4.514200 

4.520900 

4.527500 

4.534000 

4.540700 

4.547500 

4.554600 

4.562000 

4.570000 

4.578700 

4.588100 

4.598100 

4.608500 

4.619200 

4.629900 

4.640500 

4.650900 

4.660700 

4.670000 

4.678800 

4.687300 

4.695600 

4.703800 

4.711800 

4.719600 

4.727300 

Figure 50. Example of a converted sample time-concentration-discharge file created by

COMBINE for use in QTRACER (continued).

165
7.800000 7.451500 

7.900000 7.484700 

8.000000 7.500000 

8.100000 7.430900 

8.200000 7.284400 

8.300000 7.050300 

8.400000 6.737100 

8.500000 6.387400 

8.600000 6.007600 

8.700000 5.620800 

10.10000 1.955300 

10.20000 1.822500 

10.30000 1.692300 

10.40000 1.570300 

10.50000 1.457600 

10.60000 1.356800 

10.70000 1.268200 

10.80000 1.195500 

10.90000 1.141200 

11.00000 1.100000 

11.10000 1.071200 

11.20000 1.047600 

11.30000 1.025400 

11.40000 1.005700 

11.50000 0.9883500 

11.60000 0.9730800 

11.70000 0.9597900 

11.80000 0.9482800 

11.90000 0.9384500 

12.00000 0.9300100 

12.10000 0.9227900 

12.20000 0.9165100 

12.30000 0.9110100 

12.40000 0.9060800 

12.50000 0.9016000 

12.60000 0.8973800 

12.70000 0.8932800 

12.80000 0.8891300 

4.735000 

4.742500 

4.750000 

4.757300 

4.764400 

4.771400 

4.778200 

4.785000 

4.791800 

4.798600 

4.898200 

4.893100 

4.885300 

4.875300 

4.863600 

4.850900 

4.837600 

4.824400 

4.811600 

4.800000 

4.788900 

4.777400 

4.765600 

4.753600 

4.741400 

4.729000 

4.716700 

4.704300 

4.692100 

4.680000 

4.667900 

4.655700 

4.643300 

4.631000 

4.618600 

4.606400 

4.594400 

4.582600 

Figure 50. Example of a converted sample time-concentration-discharge file created by

COMBINE for use in QTRACER (continued).

166
12.90000 0.8846500 

13.00000 0.8800000 

13.10000 0.8752000 

13.20000 0.8703700 

13.30000 0.8657300 

13.40000 0.8611100 

13.50000 0.8564400 

13.60000 0.8516700 

13.70000 0.8467000 

13.80000 0.8414800 

13.90000 0.8359200 

14.00000 0.8300000 

14.10000 0.8236400 

14.20000 0.8168800 

14.30000 0.8097300 

14.40000 0.8022000 

14.50000 0.7943200 

14.60000 0.7860800 

14.70000 0.7775200 

14.80000 0.7686500 

14.90000 0.7594700 

15.00000 0.7500100 

15.10000 0.7403100 

15.20000 0.7302900 

15.30000 0.7199100 

15.40000 0.7090900 

15.50000 0.6977200 

15.60000 0.6857500 

15.70000 0.6730600 

15.80000 0.6596100 

15.90000 0.6454500 

16.00000 0.6300200 

16.10000 0.6125300 

16.20000 0.5931100 

16.30000 0.5713600 

16.40000 0.5479400 

16.50000 0.5234300 

16.60000 0.4982300 

4.571100 

4.560000 

4.549400 

4.539300 

4.529500 

4.519900 

4.510500 

4.501000 

4.491300 

4.481400 

4.471000 

4.460000 

4.448300 

4.435800 

4.422800 

4.409400 

4.395800 

4.382100 

4.368500 

4.355200 

4.342300 

4.330000 

4.318200 

4.306700 

4.295300 

4.284200 

4.273200 

4.262400 

4.251700 

4.241000 

4.230500 

4.220000 

4.209700 

4.199700 

4.189900 

4.180200 

4.170500 

4.160900 

Figure 50. Example of a converted sample time-concentration-discharge file created by

COMBINE for use in QTRACER (continued).

167
16.70000 0.4728200 

16.80000 0.4476800 

16.90000 0.4236500 

17.00000 0.4000200 

17.10000 0.3764900 

17.20000 0.3527600 

17.30000 0.3281100 

17.40000 0.3034000 

17.50000 0.2790800 

17.60000 0.2556700 

17.70000 0.2335400 

17.80000 0.2133000 

17.90000 0.1956400 

18.00000 0.1800100 

18.10000 0.1664700 

18.20000 0.1541500 

18.30000 0.1424000 

18.40000 0.1314100 

18.50000 0.1211600 

18.60000 0.1116100 

18.70000 0.1027500 

18.80000 9.4541997E-02 

18.90000 8.7022997E-02 

19.00000 8.0007002E-02 

19.10000 7.3376998E-02 

19.20000 6.7073002E-02 

19.30000 6.0977999E-02 

19.40000 5.5206001E-02 

19.50000 4.9722001E-02 

19.60000 4.4805001E-02 

19.70000 4.0520001E-02 

19.80000 3.6550999E-02 

19.90000 3.3009000E-02 

20.00000 3.0003000E-02 

4.151000 

4.141000 

4.130700 

4.120000 

4.108800 

4.097000 

4.084900 

4.072500 

4.060000 

4.047500 

4.035100 

4.023000 

4.011200 

4.000000 

3.989300 

3.978800 

3.968700 

3.958700 

3.948900 

3.939100 

3.929400 

3.919700 

3.909900 

3.900000 

3.890000 

3.880000 

3.870000 

3.860000 

3.850000 

3.840000 

3.830000 

3.820000 

3.810000 

3.800000 

Figure 50. Example of a converted sample time-concentration-discharge file created by

COMBINE for use in QTRACER (continued).

168
Figure 51. Plot of the Combine.out data listed in Figure 50.

169
in a very large file with a very small time spacing. This small time spacing results in a

total of 185 data values (using a 0.1 interpolation step). Therefore, the solid and dashed

lines actually plot as smooth curves rather than as a series of straight-line segments between

data points. From this perspective the quality of the plot indicates that the data listed in

Figure 50 would be acceptable for analysis by QTRACER.

10.4.2. COMBINE Processing

To be able to produce matching time-concentration and time-discharge data files COMBINE

interpolates both data sets independently to produce two new, very large data files. These

are then written to temporary storage and read back into the program in truncated form.

The temporary storage can occupy considerable storage space so it is necessary that the user

ensure that adequate storage space exists on the hard drive prior to running COMBINE.

By truncating the actual data, it is more likely that matching time values for the timeconcentration and time-discharge data files will be obtained than if the entire data record

were to be read. If the entire data record were to be read, it is probable that extraneous

decimal places in the time-concentration and time-discharge data files could not be found

to match. The new time-concentration-discharge file is then written to the hard drive and

the temporary files deleted.

10.4.3. COMBINE Source

The FORTRAN source code is included on the COMBINE disk. Modification of the COMBINE main file can be relatively easily accomplished if desired, but is not recommended.

The user should not attempt to modify the included subroutines.

170
11. CONCLUSIONS

Tracer-breakthrough curves developed from quantitative hydrological tracer tests can be

evaluated given the present high level of accuracy of analytical fluorescence chemistry (and

other tracer substances) and efficiency of numerical algorithms available. Ground-water

flow directions, velocities, and related hydraulic processes such as dispersion, divergence,

convergence, dilution, and storage can be properly established from tracer studies and can

be used to devise better structural models of the karst aquifer. Because of the lack of

physical access to caves at many karst sites, these structural models can be valuable for

predicting ground-water flow and contaminant transport in the aquifer.

From a human health perspective, quantitative ground-water tracing studies can assist in

demonstrating real connections between tracer injection sites and downgradient receptors.

Residence times and tracer velocities can provide ground-water managers with potential

time-of-travel estimates likely to occur for nonreactive pollutant spills in the vicinity of

tracer injection sites. Pollutant mass dispersion, dilution, and related processes can also

be estimated by such studies. Until such time that conduit accessibility becomes a reality,

ground-water tracing studies provide the best alternative to acquiring hydraulic data for

karst and fractured-rock aquifers.

A robust, efficient, easy-to-use computer program, QTRACER2, and two related computer programs, NDATA and AUTOTIME, facilitate the analysis of tracer-breakthrough

curves. All three programs are well documented. It is expected that in the future, quantitative tracing of contaminated sites will become more and more important for parameter

estimation. QTRACER2 will enhance the necessary analyses and lead to improved site

evaluations.

171
NOTATION

A bulk flow region cross-sectional area (L2)

A matrix of time values used in the Chatwin analysis (T)

AI accuracy index (dimensionless)

Ap constant of proportionality for amount of diffusing material (M T1/2 L−3)

As karst conduit surface (L2)

b vector of concentration parameters for the Chatwin analysis (T1/2)

C tracer concentration (M L−3)

C0 initial tracer concentration (M L−3)

Cb average tracer background concentration (M L−3)

C average solute (tracer) concentration (M L−3)

Cf final tracer concentration (M L−3)

Cif final measured tracer concentration corrected for background (M L−3)

Cii initial measured tracer concentration uncorrected for background (M L−3)

Ci average concentration of tracer input over time interval (M L−3)

Cp peak tracer concentration (M L−3)

CpL steady-state (plateau) tracer concentration at a resurgence

for repeated instantaneous injections (M L−3)

C (xs, t) mass of recovered tracer over distance(s), xs and time(s), t [M L−3];

D steady-state tracer dilution for multiple injections (dimensionless)

DC karst conduit diameter (L)

DH karst conduit hydraulic depth (L)

DL longitudinal dispersion coefficient (L2 T−1)

Dm molecular diffusion coefficient (L2 T−1)

ff friction factor (dimensionless)

F cumulative residence time distribution (dimensionless)

g gravitational acceleration (L T−2)

hL hydraulic head loss (L)

kf mass transfer coefficient (L T−1)

K equivalent hydraulic conductivity for laminar flow (L T−1)

Ka karst conduit sorption coefficient (L)

m karst conduit roughness correction factor (dimensionless)

172
NOTATION cont. 

Min mass of tracer injected (M)

Mm mass of multiple tracer injections (M)

MO mass of tracer recovered (M)

MT total tracer mass recovered from all sampling stations (M)

n number of measured data points (dimensionless)

ne effective fracture porosity (dimensionless)

NF Froude number (dimensionless)

NR Reynolds number (dimensionless)

Nsc Schmidt number (dimensionless)

Nsh Sherwood number number (dimensionless)

P e P ́eclet number (dimensionless)

Q ground-water discharge (L3 T−1)

Q mean ground-water discharge (L3 T−1)

r karst conduit radius (L)

Sd sinuosity factor (dimen.)

t time of sample collection (T)

tc time conversion factor (T)

Td duration in time for tracer cloud to pass any one point in the flow section (T)

TD duration in time required for entire tracer cloud to pass a flow section (T)

Te elapsed time to leading edge of tracer cloud (T)

Tf elapsed time to trailing edge of tracer cloud (T)

tinf time tracer takes to reach the flow system (T)

t2 time for tracer injection for a pulse injection (T)

tκ maximum allowable time for Chatwin analysis (T)

tp time to peak concentration (T)

t

 ̄ mean tracer residence time (T)

∆t time interval between multiple tracer injections (T)

υ ̄ mean tracer velocity (L T−1)

υp peak tracer velocity (L T−1)

υs shear tracer velocity (L T−1)

xs radial distance to sampling station (L)

173
NOTATION cont. 

V volume of individual karst conduits or fractures (L3)

VT total volume space occupied by open space used for tracer migration L3)

w fracture width (L)

x straight-line tracer migration distance (L)

x vector of straight-line parameters used in the Chatwin analysis (T1/2)

x vector of straight-line parameters used in the Chatwin analysis (T1/2)

xs sinuous tracer migration distance (L)

δ laminar flow sublayer (L)

δm molecular diffusion layer thickness (L)

γt skewness coefficient (T3)

κt kurtosis coefficient (T4)

ε relief of karst conduit wall surface irregularities (L)

μ dynamic viscosity (M L−1T−1)

π pi (dimensionless)

ρ fluid density (M L−3)

σt standard deviation for mean residence time (T)

συ standard deviation for mean flow velocity (L T−1)

174
REFERENCES

Atkinson, T.C. (1977) Diffuse flow and conduit flow in limestone terrain in the Mendip Hills,

Somerset (Great Britain). J. Hydrol. 35;93–110.

Atkinson, T.C. (1987) Karst Hydrology Course Manual. Karst Field Studies at Mammoth Cave,

Center for Cave and Karst Studies. Western Kentucky University and Mammoth Cave National

Park.

Atkinson, T.C., Smith, D.I., Lavis, J.J., and Whitaker R.J. (1973) Experiments in tracing

underground waters in limestones. J. Hydrol. 19;323–349.

Barczewski, B. and Marshall, P. (1992) Development and application of a lightfibre fluorometer for

tracer tests. Tracer Hydrology. H. Hotzl  ̈ and A. Werner, eds. Rotterdam, Netherlands: A.A.

Balkema;33–39.

Behrens, H. (1986) Water tracer chemistry: A factor determining performance and anlytics of

tracers. 5th International Symposium on Underground Water Tracing;121–133.

Bencala, K.E. and Waters, R.A. (1983) Simulation of solute transport in a mountain pool-and-riffle

stream, A transient storage model. Water Resour. Res. 19(3);718–724.

Benischke, R. and Leitner, A. (1992) Fiberoptic fluorescence sensors — An advanced concept for

tracer hydrology. Tracer Hydrology. H. Hotzl  ̈ and A. Werner, eds. Rotterdam, Netherlands;

A.A. Balkema;41–47.

Brady, J.A., and Johnson, P. (1981) Predicting times of travel, dispersion and peak concentrations

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